Prof. RNDr. Irena Rachunkova, DrSc.   Department of Mathematical Analysis and Applications of Mathematics Faculty of Science Palacky University e-mail: rachunko@inf.upol.cz

Education and degrees

• graduated from Faculty of Science, Palacky University, in numerical mathematics (1970)
• 1970 RNDr. (Doctor of Natural Sciences), Faculty of Science, Palacky University, in algebra and number theory
• 1976 CSc. (PhD) Palacky 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, Palacky University, in mathematical analysis

Employment

Research

List of publications

2009 + accepted

1. I. Rachůnková, G. Pulverer, E. Weinmüller: A unified aproach to singular problems arising in the membrane theory. Applications of Mathematics. Accepted. PDF
2. L. Rachůnek, I. Rachůnková: Approximation of differential problems with singularities and time discontinuities. Nonlinear Analysis (WCNA 2008). Accepted. PDF
3. I. Rachůnková, J. Tomeček: Singular nonlinear problem for ordinary differential equation of the second-order on the half-line. Santiago de Compostela, 2008. Accepted. PDF
4. I. Rachůnková, S. Staněk, M. Tvrdý: Solvability of Nonlinear Singular Problems for Ordinary Differential Equations. Hindawi Publishing Corporation, New York, USA, in press.
5. 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.
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.
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.
2. I. Rachůnková, S. Staněk: Topological degree methods in functional boundary value problems at resonance, Nonlinear Anal. TMA 27 (1996), 271-285.
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.
3. I. Rachůnková: Boundary value problems with nonlinear conditions, Acta Math. Inf. Univ. Ostrav. 2 (1994), 71-77.

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.
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

Ceska verze

17. 11. 2006, Irena Rachunkova, Lukas Rachunek