Česká verze

Prof. RNDr. Irena Rachůnková, DrSc.   Department of Mathematical Analysis and Applications of Mathematics Faculty of Science Palacký University e-mail: irena.rachunkova@upol.cz

Education and degrees

• graduated from Faculty of Science, Palacký University, in numerical mathematics (1970)
• 1970 RNDr. (Doctor of Natural Sciences), Faculty of Science, Palacký University, in algebra and number theory
• 1976 CSc. (Ph.D.) Palacký University, in mathematical analysis
• 1985 associate professor, Palacky University, in mathematical analysis
• 1996 DrSc. (Doctor of Sciences), Mathematical Institute of the Czech Academy of Sciences, Prague, in mathematical analysis
• 1998 professor, Palacký University, in mathematical analysis

Employment

Bachelor theses

New topics

1. Population dynamical models
2. Epidemic dynamical models
3. Economical dynamical models
4. Rotated pendulum
5. Oscillators
6. Gradient systems

Present theses

• V. Durdyová: May's population model

Accepted theses

• 2018 - A. Čulíková: Epidemic dynamical models
• 2013 - Ž. Vančurová: Continuous multiplicator-accelerator model
• 2013 - K. Halouzková: Smith's model of harvesting strategy
• 2013 - P. Běhalová: Predator-prey model
• 2012 - K. Dvorská: Phase portraits of mathematical pendulum
• 2010 - L. Kozelková: IS-LM model of the economy
• 2010 - J. Studnička: Gompertz population equation
• 2009 - D. Cahová: Matematical model eutrophication of lake Mendota
• 2009 - Z. Červenková: Dynamical systems and their applications
• 2009 - M. Dvorská: Local extrema of implicit functions
• 2007 - J. Stankuš: Diskrete population models
• 2003 - K. Machová: Genetic dynamical models
• 2003 - H. Pecinová: Dynamical systems in social sciences
• 2003 - Existence and uniqueness of solutions of BVPs of second order ODEs
• 2003 - M. Blažej: Discrete population models
• 2002 - M. Jamborová: Application of the theory of dynamical systems in finances
• 2001 - K. Jurečková: Discrete dynamical systems and their application in population growth models
• 2001 - K. Ptáčková: Stair-step diagrams and their application in harvesting strategy models
• 2000 - K. Tobolová: Discrete dynamical modeling
• 2000 - H. Pichlová: Linear dynamical systems and their application in social sciences
• 1999 - A. Ondruchová: Linear dynamical systems and their application in genetics
• 1998 - J. Ondráčková: Dynamical systems of the first order

Master theses

New topics

1. Impulsive initial value problem for ordinary differential equations
2. Impulsive boundary value problem for ordinary differential equations

Present theses

• K. Dudková: Differential equations with impulses
• J. Kalas: Mathematical modelling and integral equations

Accepted theses

• 2018 - L. Horáčková: Stable and unstable manifolds of planar dynamical systems
• 2016 - Š. Dedinský: Impulsive initial problem for ordinary differential equations
• 2015 - K. Daňková: Damped pendulum with torque
• 2012 - I. Stejskalová: Elementary bifurcations of dynamical systems
• 2007 - B. Beníšková: Topological methods in the theory of BVPs of differential equations
• 2005 - L. Fenclová: Dynamical systems and their application in epidemiology
• 2004 - I. Mikešová: Population models
• 2004 - J. Tomeček: Nonlinear BVPs for differential equations with impulses
• 2003 - Periodic boundary value problems
• 2003 - V. Polášek: Impulsive periodic problem
• 2002 - J. Wyzulová: Nonhyperbolic critical points of dynamical systems
• 2002 - R. Urbánek: Existence and uniqueness of solutions of BVPs of ODEs
• 2000 - S. Salcburgerová: Macroeconomical models
• 2000 - H. Tománková: BVPs of differential equations of the second order on infinite interval
• 1999 - R. Literák: BVPs of ordinary differential equations of the second order
• 1998 - Nováčková: Mathematical modeling and differential equations
• 1998 - M. Dvořáková: Differential equations ? dynamical systems approach
• 1997 - Asymptotic properties of solutions of ODEs of the second order
• 1996 - H. Krejčí: Dynamical systems and their application in economics
• 1996 - M. Hájek: Periodical solutions of differential systems
• 1995 - I. Štěrbová: Dynamical systems and their application
• 1995 - J. Marek: Dynamical systems and bifurcations
• 1994 - M. Pallová: Asymptotic properties of solutions of ODEs and program PHASER
• 1994 - D. Vlčková: BVPs of ODEs and program PHASER
• 1993 - T. Palkovský: Topological methods of the study of BVPs

Disertation theses

Accepted theses

• 2017 - Martin Rohleder: Boundary value problems with time singularity
• 2015 - Jana Burkotová: Asymptotic behaviour of differential models
• 2012 - Jakub Stryja: Singular Dirichlet problems for differential equation of the second order
• 2007 - Jan Tomeček: Impulsive boundary value problems
• 2006 - Vladimír Polášek: Boundary value problems with phi-Laplacian
• 2005 - Jan Draessler: Periodic boundary value problem for ordinary second order differential equations
• 1998 - Pavel Calábek: Boundary value problems for systems of second order differential equations
• 1992 - Martin Šenkyřík: On a third-order three-point nonlinear boundary value problem

Grants

• 2014-2016: GAČR 14-06958S - "Singularities and impulses in boundary value problems for nonlinear ordinary differential equations"
• 2013-2015: CZ.1.07/2.2.00/28.0141 - "Streamling the Mathematics Studies at the Faculty of Science of Palacky University Olomouc"
• 2013-2015: CZ.1.07/2.3.00/30.0041 - "Support the creation of excellent research teams and intersectoral mobility at Palacky University in Olomouc II"
• 2005-2011: MSM 6198959214 - Research project "Mathematical Models and Structures"
• 2007-2009: GAAV IAA100190703 - "Singular nonlinear boundary value problems"
• 2004-2006: GAČR 201/04/1077 - "Qualitative analysis of solutions of ordinary and functional differential equations"
• 2003-2005: RP MŠMT - "Realization of the bachelor study program Mathematics and its Applications"
• 1999-2004: MSM 153100011 - Research project "Development of structural theory of algebraical and geometrical systems, theoretical and numerical analysis of mathematical models"
• 2001-2003: GAČR 201/01/1451 - "Qualitative analysis of ordinary and functional differential equations"
• 2000: FRVŠ 158/2000 - "Differential equations, dynamical systems and their applications"
• 1998-2000: GAČR 201/98/0318 - "Qualitative analysis of ordinary and functional differential equations"
• 1998: PG 98 479 - "Qualitative properties of solutions of functional and ordinary differential equations"
• 1997: PG 97 207 - "Qualitative properties of solutions of functional and ordinary differential equations"
• 1996: FRVŠ - "Dynamical systems, boundary value problems and their applications II"
• 1995: FRVŠ - "Dynamical systems, boundary value problems and their applications I"

Research

List of publications

2018 + accepted

1. I. Rachůnková, J. Tomeček: Equivalence between distributional differential equations and periodic problems with state-dependent impulses. EJQTDE 2 (2018), 1-22.
2. W. Auzinger, J. Burkotová, I. Rachůnková, V. Wenin: Shooting methods for state-dependent impulsive boundary value problems with applications. Applied Numerical Mathematics 128 (2018), 217-229.
3. J. Burkotová, I. Rachůnková, S. Staněk, E. Weinmüller, S. Wurm: On nonlinear singular BVPs with nonsmooth data. Part 1: Analytical results. Applied Numerical Mathematics 130 (2018), 23-50.
4. I. Rachůnková, J. Tomeček: Distributional van der Pol equation with state-dependent impulses. Lithuanian Mathematical Journal 58 (2018), 185-197.
5. L. Rachůnek, I. Rachůnková: Homoclinic solutions of singular differential equations with phi-Laplacian. EJQTDE 72 (2018), 1-19.

2017

1. J. Burkotová, I. Rachůnková, E. B. Weinmüller: On singular BVPs with unsmooth data. Analysis of the linear case with variable coefficient matrix. Applied Numerical Mathematics 114 (2017), 77-96. PDF
2. A. Rontó, I. Rachůnková, M. Rontó, L. Rachůnek: Investigation of solutions of state-dependent multi-impulsive boundary value problem. Georgian Mathematical Journal (2017) 24 (2): 287-312. PDF
3. I. Rachůnková, J. Tomeček: Antiperiodic solution of van der Pol equation with state-dependent impulses. Electronic Journal of Differential Equations 247 (2017), 1-17.
4. J. Burkotová, I. Rachůnková, E. B. Weinmüller: On singular BVPs with unsmooth data. Convergence of the collocation schemes. BIT Numer. Math. (2017) 57: 1153-1184.
5. I. Rachůnková, J. Tomeček: Impulsive problems and distributional differential equations. Functional differential equations 24 (2017), 111-126.

2016

1. J. Burkotová, I. Rachůnková, M. Rohleder, J. Stryja: Existence and uniqueness of damped solutions of singular IVPs with phi-Laplacian. EJQTDE 121 (2016) 1-28. PDF
2. I. Rachůnková, L. Rachůnek, A. Rontó, M. Rontó: A constructive approach to boundary value problems with state-dependent impulses. Applied Mathematics and Computation 274 (2016) 726-744. PDF
3. J. Burkotová, M. Hubner, I. Rachůnková, E. B. Weinmüller: Asymptotic properties of Kneser solutions to nonlinear second order ODE with regularly varying coefficients. Applied Mathematics and Computation 274 (2016) 65-82. PDF

2015

1. I. Rachůnková, J. Tomeček: State-Dependent Impulses: Boundary Value Problems on Compact Interval. Atlantis Press, Paris 2015.
2. I. Rachůnková, J. Stryja: Lower and upper functions in singular Dirichlet problem with phi-Laplacian. Mathematical Notes 97, 4 (2015), 588-597. PDF
3. J. Burkotová, I. Rachůnková, S. Staněk, E. B. Weinmüller: Analytical and numerical treatment of singular linear BVPs with unsmooth inhomogeneity. AIP Conf. Proc., Vol. 1648, Rhodos, 2014.
4. I. Rachůnková, J. Tomeček: Fixed point problem associated with state-dependent impulsive boundary value problems. AIP Conf. Proc., Vol 1648, Rhodos, 2014.

2014

1. I. Rachůnková, J. Tomeček: Existence principle for BVPs with state-dependent impulses. Topol. Methods in Nonlin. Analysis 44, 2 (2014), 349-368. PDF
2. I. Rachůnková, J. Tomeček: Second order BVPs with state-dependent impulses via lower and upper functions. Central European Journal of Mathematics 12, 1 (2014), 128-140. PDF
3. I. Rachůnková, J. Tomeček: Existence principle for higher order nonlinear differential equations with state-dependent impulses via fixed point theorem. Boundary Value Problems 2014, 2014:118, 15 pp. PDF
4. J. Gchwindl, I. Rachůnková, S. Staněk, E. Weinmüller: Positive blow-up solutions to nonlinear models from real world dynamics. Boundary Value Problems 2014, 2014:121, 23 pp. PDF
5. J. Burkotová, I. Rachůnková, S. Staněk, E. Weinmüller: On linear ODEs with a time singularity of the first kind and unsmooth inhomogeneity. Boundary Value Problems 2014, 2014:183, 34 pp. PDF
6. I. Rachůnková, J. Tomeček: Fixed point problem associated with state-dependent impulsive boundary value problems. Boundary Value Problems 2014, 2014:172, 17 pp. PDF
7. I. Rachůnková et al.: A tribute to Ivan Kiguradze. Boundary Value Problems 2014, 2014:228, 11 pp. PDF

2013

1. I. Rachůnková, S. Staněk: Properties of the set of positive solutions to Dirichlet boundary value problems with time singularities. Central European Journal of Mathematics 11 (1) (2013), 112-132. PDF
2. I. Rachůnková, A. Spielauer, S. Staněk, E. Weinmüller: The structure of a set of positive solutions to Dirichlet BVPs with time and space singularities. Georgian Math. J. 20 (1) (2013), 95-127. PDF
3. I. Rachůnková, J. Tomeček: New approach to BVPs with state-dependent impulses. Boundary Value Problems 2013, 2013: 22, 13 pp. PDF
4. I. Rachůnková, A. Spielauer, S. Staněk, E. Weinmüller: Positive solutions of nonlinear Dirichlet BVPs in ODEs with time and space singularities. Boundary Value Problems 2013 2013:6, 22 pp. PDF
5. I. Rachůnková, J. Tomeček: Impulsive system of ODEs with general linear boundary conditions. Electronic Journal of Qualitative Theory of Differential Equations 25 (2013), 1-16. PDF
6. L. Rachůnek, I. Rachůnková: First order nonlinear differential equations with state-dependent impulses. Boundary Value Problems 2013, 2013: 195, 18 pp. PDF

2011

1. L. Rachůnek, I. Rachůnková: Homoclinic solutions of non-autonomous difference equations arising in hydrodynamics. Nonlinear Analysis: Real World Applications 12 (2011), 14-23. PDF
2. L. Rachůnek, I. Rachůnková: On a homoclinic point of some autonomous second-order difference equation. Journal of Difference Equations and Applications 17 (2011), 753-764. PDF
3. I. Rachůnková, L. Rachůnek, J. Tomeček: Existence of oscillatory solutions of singular nonlinear differential equations. Abstract and Applied Analysis. Vol. 2011, Article ID 408525, 20 pages. PDF
4. I. Rachůnková, L. Rachůnek: Asymptotic formula for oscillatory solutions of some singular nonlinear differential equation. Abstract and Applied Analysis. Vol. 2011, Article ID 981401, 9 pages. PDF
5. A. Feichtinger, I. Rachůnková, S. Staněk, E. Weinmüller: Periodic BVPs in ODEs with time singularities. Computers and Mathematics with Applications 62 (2011), 2058-2070. PDF
6. I. Rachůnková: Asymptotic properties of homoclinic solutions of some singular nonlinear differential equations. Memoirs on Differential Equations and Math. Physics 54 (2011), 83-98. PDF

2010

1. I. Rachůnková, G. Pulverer, E. Weinmüller: A unified aproach to singular problems arising in the membrane theory. Applications of Mathematics 55 (2010), 47-75. PDF
2. I. Rachůnková, S. Staněk, E. Weinmüller, M. Zenz: Neumann problems with time singularities. Computers and Mathematics with Applications 60 (2010), 722-733. PDF
3. L. Rachůnek, I. Rachůnková: Homoclinic solutions of non-autonomous difference equations arising in hydrodynamics. Nonlinear Analysis: Real World Applications 12 (2011), 14-23. PDF
4. I. Rachůnková, J. Tomeček: Bubble-type solutions of nonlinear singular problems. Mathematical and Computer Modelling 51 (2010), 658-669. PDF
5. I. Rachůnková, J. Tomeček: Strictly increasing solutions of a nonlinear singular differential equation arising in hydrodynamics. Nonlinear Analysis 72 (2010), 2114-2118. PDF
6. L. Rachůnek, I. Rachůnková: Strictly increasing solutions of non-autonomous difference equations arising in hydrodynamics. Advances in Difference Equations, Recent Trends in Differential and Difference Equations. Vol. 2010, Article ID 714891, 11 pages. PDF
7. I. Rachůnková, J. Tomeček, J. Stryja: Oscillatory solutions of singular equations arising in hydrodynamics. Advances in Difference Equations, Recent Trends in Differential and Difference Equations. Vol. 2010, Article ID 872160, 13 pages. PDF

2009

1. L. Rachůnek, I. Rachůnková: Approximation of differential problems with singularities and time discontinuities. Nonlinear Analysis, TMA 71 (2009), e1448-e1460. PDF
2. I. Rachůnková, J. Tomeček: Homoclinic solutions of singular nonautonomous second order differential equations. Boundary Value Problems. Vol. 2009, Article ID 959636, 21 pages. PDF
3. I. Rachůnková, J. Tomeček: Singular problems on the half-line. Acta Univ. Palacki. Olomuc., Fac. rer. nat., Mathematica 48 (2009), 109-128. PDF
4. I. Rachůnková, J. Tomeček: Singular nonlinear problem for ordinary differential equation of the second-order on the half-line. Mathematical Models in Engineering, Biology, and Medicine, Proceedinngs of the International Conference on Boundary Value Problems, edited by A. Cabada, E. Lis and J. J. Nieto, (2009), 294-303. PDF
5. I. Rachůnková, S. Staněk, M. Tvrdý: Solvability of Nonlinear Singular Problems for Ordinary Differential Equations. Hindawi Publishing Corporation, New York, USA, 2009, 268 pages. PDF
6. I. Rachůnková, S. Staněk, E. Weinmüller, M. Zenz: Limit properties of solutions of singular second-order differential equations. Boundary Value Problems, Vol. 2009, Article ID 905769, 28 pages. PDF
7. I. Rachůnková, L. Rachůnek: Singular discrete and continuous mixed boundary value problems. Math. Comp. Modelling 49 (2009), 413-422. PDF

2008

1. I. Rachůnková, L. Rachůnek: Singular discrete problem arising in the theory of shallow membrane caps. Journal of Difference Equations and Applications 14 (2008), 747-767. PDF
2. I. Rachůnková, J. Stryja: Dirichlet problem with phi-Laplacian and mixed singularities. Nonlinear Oscillations 11 (2008), 81-95. PDF

2007

1. I. Rachůnková, J. Stryja: Singular Dirichlet boundary value problem for second order ODE. Georgian Math. Journal 14 (2007), 325-340. PDF
2. I. Rachůnková, L. Rachůnek: Solvability of discrete Dirichlet problem via lower and upper functions method. Journal of Difference Equations and Applications 13 (2007), 423-429. PDF
3. I. Rachůnková, C. C. Tisdell: Existence of non-spurious solutions to discrete Dirichlet problems with lower and upper solutions. Nonlinear Analysis 67 (2007), 1236-1245. PDF
4. I. Rachůnková, O. Koch, G. Pulverer, E. Weinmüller: On a singular boundary value problem arising in the theory of shallow membrane caps. J. Math. Anal. Appl. 332 (2007), 523-541. PDF
5. D. R. Anderson, I. Rachůnková, C. C. Tisdell: Solvability of discrete Neumann boundary value problems. J. Math. Anal. Appl. 331 (2007), 736-741. PDF
6. I. Rachůnková, J. Tomeček: Singular nonlinear problem for ordinary differential equation of the second order. Acta Univ. Palacki. Olomuc., Fac. rer. nat., Mathematica 46 (2007), 75-84. PDF

2006

1. I. Rachůnková: Singular mixed boundary value problem. J. Math. Anal. Appl. 320 (2006), 611-618. PDF
2. I. Rachůnková, J. Tomeček: Singular Dirichlet problem for ordinary differential equation with impulses. Nonlinear Analysis 65 (2006), 210-229. PDF
3. I. Rachůnková, S. Staněk, M. Tvrdý: Singularities and Laplacians in Boundary Value Problems for Nonlinear Ordinary Differential Equations. Handbook of Differential Equations. Ordinary Differential Equations, vol.3, pp. 607-723. Ed. by A. Cañada, P. Drábek, A. Fonda. Elsevier 2006. PDF
4. V. Polášek, I. Rachůnková: Singular periodic problem for nonlinear ordinary differential equations with phi-Laplacian. Electronic J. Differential Equations, Vol.2006 (2006), No. 27, pp. 1-12. PDF
5. I. Rachůnková: Strong singularities in mixed boundary value problems. Mathematica Bohemica 131 (2006), 393-409. PDF
6. I. Rachůnková, L. Rachůnek: Singular discrete second order BVPs with p-Laplacian. Journal of Difference Equations and Applications 12 (2006), 811-819. PDF
7. I. Rachůnková, C. C. Tisdell: Existence of non-spurious solutions to discrete boundary value problems. Australian Journal of Mathematical Analysis and Applications 3 (2006), 1-9. PDF
8. I. Rachůnková: Superlinear mixed BVP with time and space singularities. Conference Proceedings CDDEA 2005, Hindawi Publ. Corporation, Eds. R. P. Agarwal, K. Perera, 2006, pp. 953-961. PDF
9. I. Rachůnková, M. Tvrdý: Periodic singular problem with quasilinear differential operator. Mathematica Bohemica 131 (2006), 321-336. PDF

2005

1. V. Polášek, I. Rachůnková: Singular Dirichlet problem for ordinary differential equations with phi-Laplacian. Mathematica Bohemica 130 (2005), 409-425. PDF
2. I. Rachůnková, M. Tvrdý: Second order periodic problems with phi-Laplacian and impulses. Proc. WCNA 2004. Nonlinear Analysis 63 (2005), e257-e266. PDF
3. I. Rachůnková, M. Tvrdý: Periodic problems with phi-Laplacian involving non-ordered lower and upper functions. Fixed Point Theory 6 (2005), 99-112. PDF
4. I. Rachůnková, M. Tvrdý: Method of lower and upper functions in impulsive periodic boundary value problems. EQUADIFF 2003, pp. 252-257. World Scientific, Singapore 2005.
5. I. Rachůnková, M. Tvrdý: Non-ordered lower and upper functions in second order impulsive periodic problems. DCDIS, Ser. A, Math. Anal. 12 (2005), 397-415. PDF

2004

1. I. Rachůnková, M. Tvrdý: Nonmonotone impulse effects in second order periodic boundary value problems. Abstr. Appl. Anal. 7 (2004), 577-590. PDF
2. I. Rachůnková, M. Tvrdý: Construction of non-constant lower and upper functions for impulsive periodic problems. Electronic J. Qualit. Th. Diff. Equations (Proc. 7th Coll. QTDE) 19 (2004), 1-8. PDF
3. I. Rachůnková, J. Tomeček: Impulsive BVPs with nonlinear boundary conditons for the second order differential equations without growth restrictions. J. Math. Anal. Appl. 292 (2004), 525-539. PDF
4. I. Rachůnková, S. Staněk: General existence principle for singular BVPs and its applications. Georgian Mathematical Journal 11 (2004), 549-565. PDF
5. I. Rachůnková, S. Staněk: A singular boundary value problem for odd order differential equations. J. Math. Anal. Appl. 291 (2004), 741-756. PDF
6. I. Rachůnková, M. Tvrdý: Existence results for impulsive second order periodic problems. Nonlin. Anal. 59 (2004), 133-146. PDF
7. I. Rachůnková, S. Staněk: Zeros of derivatives of solutions to singular (p,n-p) conjugate BVPs. Acta Univ. Palacki. Olomuc., Fac. rer. nat., Mathematica 43 (2004), 137-141. PDF

2003

1. I. Rachůnková: Singular Dirichlet second order boundary value problems with impulses. Journal Diff. Equations 193 (2003), 435-459. PDF
2. I. Rachůnková, S. Staněk: Sturm-Liouville and focal higher order BVPs with singularities in phase variables. Georgian Mathematical Journal 10 (2003), 165-191. PDF
3. I. Rachůnková, S. Staněk: Sign-changing solutions of singular Dirichlet boundary value problems. Archives of Inequalities and Applications 1 (2003), 11-30. PDF
4. I. Rachůnková, S. Staněk: Connections between types of singularities in differential equations and smoothness of solutions of Dirichlet BVPs. Dyn. Contin. Discrete Impulsive Syst. 10 (2003), 209-222. PDF
5. I. Rachůnková, M. Tvrdý, I. Vrkoč: Resonance and multiplicity in periodic boundary value problems with singularity. Mathematica Bohemica 128 (2003), 45-70. PDF
6. R. P. Agarwal, D. O'Regan, I. Rachůnková, S. Staněk: Two-point higher order BVPs with singularities in phase variables. Computers and Mathematics with Applications 46 (12) (2003), 1799-1826. PDF

2002

1. I. Rachůnková, M. Tvrdý: Localization of nonsmooth lower and upper functions for periodic boundary value problems, Math. Bohemica 127 (2002), 531-545. PDF
2. I. Rachůnková, J. Tomeček: On nonlinear boundary value problems with impulses, Mathematical Notes (Miskolc) 3 (2002), 59-69. PDF
3. I. Rachůnková, J. Tomeček: On nonlinear boundary value problems for systems of differential equations with impulses. Acta Univ. Palacki. Olomuc., Fac. rer. nat., Mathematica 41 (2002), 119-129. PDF
4. I. Rachůnková, M. Tvrdý: Impulsive periodic boundary value problem and topological degree. Functional Differential Equations No. 3-4, 9 (2002), 471-498. PDF

2001

1. I. Rachůnková: On the existence of more positive solutions of periodic BVPs with singularity, Applicable Analysis 79 (2001), 257-275. PDF
2. J. Draessler, I. Rachůnková: On three solutions of the second order periodic boundary value problem, Nonlinear Oscillations 4 (2001), 471-486. PDF
3. I. Rachůnková, M. Tvrdý: Nonlinear systems of differential inequalities and solvability of certain nonlinear second order boundary value problems, Journal Inequal. Appl. 6 (2001), 199-226. PDF
4. I. Rachůnková, M. Tvrdý: Construction of lower and upper functions and their application to regular and singular periodic boundary value problems, Nonlinear Anal. TMA 47 (2001), 6, 3937-3948. PDF
5. I. Rachůnková, M. Tvrdý, I. Vrkoč: Existence of nonnegative and nonpositive solutions for second order periodic boundary value problems, Journal Diff. Equations 176 (2001), 445-469. PDF

2000

1. I. Rachůnková: Upper and lower solutions and multiplicity results, Journal Math. Anal. Appl. 246 (2000), 449-464. PDF
2. I. Rachůnková: Existence of two positive solutions of a singular nonlinear periodic boundary value problem, Journal Comp. Appl. Math. 113 (2000), 27-34. PDF
3. I. Rachůnková, M. Tvrdý: Method of lower and upper functions and the existence of solutions to singular periodic problems for second order nonlinear differential equations, Math. Notes Miskolc 2 (2000), 135-143. PDF

1999

1. I. Rachůnková: Upper and lower solutions and topological degree, Journal Math. Anal. Appl. 234 (1999), 311-327. PDF
2. I. Rachůnková: On four-point boundary value problems without growth conditions, Czechoslovak Math. Journal 49 (1999), 241-248.

1998

1. I. Rachůnková: Topological degree methods in functional boundary value problems, Univ. Jagell. Acta Math. 36 (1998), 237-238.
2. I. Rachůnková: Topological degree, lower and upper solutions and multiplicity for functional boundary value problems, Functional Diff. Eqns 5 (1998), 403-423.

1997

1. I. Rachůnková: Upper and lower solutions satisfying the inverse inequality, Ann. Pol. Math. 65 (1997), 235-244.
2. I. Rachůnková: Multiple solutions of nonlinear boundary value problems and topological degree, Proc. EQUADIFF 9 Brno (1997), 147-158.

1996

1. I. Rachůnková, S. Staněk: Topological degree methods in functional boundary value problems, Nonlinear Anal. TMA 27 (1996), 153-166. PDF
2. I. Rachůnková, S. Staněk: Topological degree methods in functional boundary value problems at resonance, Nonlinear Anal. TMA 27 (1996), 271-285. PDF
3. I. Rachůnková: Topological degree methods in BVPs with nonlinear conditions, Ann. Math. Silesian. 11 (1996), 103-110.

1995

1. I. Rachůnková: On the existence of two solutions of the four-point problem, Journal Math. Anal. Appl. 193 (1995), 245-254.

1994

1. I. Rachůnková: On the existence of two solutions of the periodic problem for the ordinary differential equation, Nonlinear Anal. TMA 22 (1994), 1315-1322.
2. I. Rachůnková: Sign conditions in nonlinear boundary value problems, Acta Univ. Palacki. Olomuc., Fac. rer. nat., Mathematica 114 (1994), 117-124. PDF
3. I. Rachůnková: Boundary value problems with nonlinear conditions, Acta Math. Inf. Univ. Ostrav. 2 (1994), 71-77. PDF

1993

1. I. Rachůnková: On the number of solutions of the Neumann problem for the ordinary second order differential equation, Ann. Math. Silesian. 7 (1993), 79-87.

1992

1. I. Rachůnková: Multiplicity results for four-point boundary value problems, Nonlinear Anal. TMA 18 (1992), 497-505. PDF
2. I. Rachůnková: On a certain four-point problem, Radovi Matem. 8 (1992), 81-93.
3. I. Rachůnková: On some three-point problems for third-order differential equations, Math. Bohemica 117 (1992), 98-110.
4. I. Rachůnková: On a transmission problem, Acta Univ. Palacki. Olomuc., Fac. rer. nat., Mathematica 105 (1992), 45-59.

1991

1. I. Rachůnková: Multipoint boundary value problems at resonance, Fasc. Math. 23 (1991), 97-102.
2. I. Rachůnková: Periodic boundary value problems for third order differential equations, Math. Slovaca 41 (1991), 241-248.
3. I. Rachůnková: An existence theorem of the Leray-Schauder type for four-point boundary value problems, Acta Univ. Palacki. Olomuc., Fac. rer. nat., Mathematica 100 (1991), 49-59.

1990

1. I. Rachůnková: On Kneser problem for differential equations of the 3rd order, Časopis pro pěst. mat. 115 (1990), 18-27.
2. I. Rachůnková: Nonnegative nonincreasing solutions of differential equations of the 3rd order, Czechoslovak Math. Journal 40 (1990), 213- 221.
3. I. Rachůnková: 2n-point problems for differential equations of the n-th order, Journal Math. Anal. Appl. 145 (1990), 100-111.
4. I. Rachůnková: Periodic boundary value problems for second order differential equations, Acta Univ. Palacki. Olomuc., Fac. rer. nat., Mathematica 97 (1990), 83-91.

1989

1. I. Rachůnková: Existence and uniqueness of solutions of (n+1)-point value problems for differential equations of the n-th order, Ann. Mat. Pura Appl. 155 (1989), 285-298.
2. I. Rachůnková: The first kind periodic solutions of differential equations of the second order, Math. Slovaca 39 (1989), 407-415.
3. I. Rachůnková: On a certain three-point boundary value problem, Math. Slovaca 39 (1989), 417-426.
4. I. Rachůnková: A four-point problem for differential equations of the second order, Arch. Math. (Brno) 25 (1989), 175-184.
5. I. Rachůnková: Existence and uniqueness of solutions of four-point boundary value problems for 2nd order differential equations, Czechoslovak Math. Journal 39 (1989), 692-700.
6. I. Rachůnková: On certain multipoint boundary value problems, Acta Univ. Palacki. Olomuc., Fac. rer. nat., Mathematica 94 (1989), 43-60.
7. I. Rachůnková: Multipoint boundary value problems at resonance, Proc. EQUADIFF 7 Praha 1989.

1988

1. I. Rachůnková: On a nonlinear problem for third order differential equations, Acta Univ. Palacki. Olomuc., Fac. rer. nat., Mathematica 91 (1988), 225-249.
2. I. Rachůnková: On (n+1)-point boundary value problem for differential equations of the n-th order, (in Russian), Trudy IPM Tbilisi 31 (1988), 159-178.
3. I. Rachůnková: Multipoint boundary value problems for differential equations of the second order, 10-th Summer School on Differential Equations, Poprad (1988), 107-123.

1974 - 1984

1. I. Rachůnková: On the theory of phases of Academician O. Borůvka, Acta Univ. Palacki. Olomuc., Fac. rer. nat., Mathematica 45 (1974), 63-75.
2. I. Rachůnková: On algebraic properties of dispersions of the 3rd and 4th kind of differential equation y´´ = q(t)y, Časopis pro pěst. mat. 100 (1975), 15-25.
3. I. Rachůnková: On a coincindence of central dispersions of the first and second kind in connection with periodic solutions of the differential equation y´´ = q(t)y, Arch. Math. (Brno) 4 (1975), 205-216.
4. I. Rachůnková: Algebraic properties of phases of the differential equation y´´ = q(t)y, Acta Univ. Palacki. Olomuc., Fac. rer. nat., Mathematica 57 (1978), 69-76.
5. I. Kiguradze, I. Rachůnková: On the solvability of a nonlinear problem of the Kneser type, (in Russian), Diff. Uravn. 15 (1979), 1754-1765.
6. I. Rachůnková: On the Kneser problem for systems of ordinary differential equations, (in Russian), Soob. Acad. Nauk GSSR 94 (1979), 545-548.
7. I. Kiguradze, I. Rachůnková: On a certain non-linear problem for two-dimensional differential systems, Arch. Math. (Brno) 16 (1980), 15-38.
8. I. Rachůnková: On a Kneser problem for a system of nonlinear ordinary differential equations, Czechoslovak Math. Journal 31 (1981), 114-126.
9. I. Rachůnková: On one nonlinear boundary value problem for differential systems of the n-th order, (in Russian), Czechoslovak Math. Journal 34 (1984), 285-297.

Palacky University

Faculty of Science

Department of Mathematical Analysis and Applications of Mathematics

Česká verze

6. 11. 2016, Irena Rachůnková, Lukáš Rachůnek