Cílem projektu je studium kvalitativních vlastností řešení obyčejných diferenciálních rovnic, včetně rovnic se zpožděným argumentem. Speciální pozornost bude věnována studiu diferenciálních rovnic modelujících reálné problémy

Description in English
Project is a continuation of the projects IAA1163401 GA AV (2004-2006) a 201/08/0469 GA ČR (2008-2010). The main attention will be focused on the following problems of the qualitative theory of differential equations: Asymptotic properties of solutions of differential equations with general Phi-Laplacian; To built relative oscillation theory for half-linear differential equations; Asymptotic and oscillatory properties of solutions of delayed differential equations; Stability of delayed differential systems; Numerical investigation of the first order delayed differential equations; Applications of some derived results to differential equations modelling problems of a technical or scientific nature

Keywords
obyčejné diferenciální rovnice; asymptotické vlastnosti; oscilace; odkloněný argument; diskretizační me

Key words in English
obyčejné diferenciální rovnice; asymptotické vlastnosti; oscilace; odkloněný argument; diskretizační me

GAP201/11/0768

Czech

Došlá Zuzana, Prof. RNDr., DrSc. - principal person responsible
Čermák Jan, prof. RNDr., CSc. - fellow researcher

Institute of Mathematics
- responsible department (1.1.1989 - not assigned)
Institute of Mathematics
- co-beneficiary (1.1.2011 - 31.12.2015)

SVOBODA, Z. Representation of Solutions of Linear Differential Systems of the Second Order with Constant Delays. Journal of Mathematical Sciences, 2017, vol. 222, no. 3, p. 345-358. ISSN: 1072-3374.
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SIEGMUND, S.; DIBLÍK, J.; NOWAK, C. A generalized Picard-Lindelöf theorem. Electronic Journal of Qualitative Theory of Differential Equations, 2016, vol. 2016, no. 28, p. 1-8. ISSN: 1417-3875.
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ČERMÁK, J.; JÁNSKÝ, J. Stability and periodic investigations of linear planar difference systems. MATHEMATICAL METHODS IN THE APPLIED SCIENCES, 2016, vol. 39, no. 18, p. 5343-5354. ISSN: 0170-4214.
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TOMÁŠEK, P. Asymptotic stability regions for certain two parametric full-term linear difference equation. In Differential and Difference Equations with Applications. Springer Proceedings in Mathematics & Statistics. Springer Proceedings in Mathematics and Statistics. New York: Springer, 2016. p. 323-330. ISBN: 978-3-319-32855-3. ISSN: 2194-1009.
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ČERMÁK, J.; KISELA, T.; HORNÍČEK, J. Stability regions for fractional differential systems with a time delay. Communications in Nonlinear Science and Numerical Simulation, 2016, vol. 31, no. 1-3, p. 108-123. ISSN: 1007-5704.
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ČERMÁK, J. Stability conditions for linear delay difference equations: A survey and perspectives. Tatra Mountains Mathematical Publications, 2015, vol. 63, no. 63, p. 1-29. ISSN: 1210-3195.
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ČERMÁK, J.; NECHVÁTAL, L.; GYŐRI, I. On explicit stability conditions for a linear fractional difference system. Fractional Calculus and Applied Analysis, 2015, vol. 18, no. 3, p. 651-672. ISSN: 1311-0454.
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KISELA, T.; ČERMÁK, J. Stability properties of two-term fractional differential equations. NONLINEAR DYNAMICS, 2015, vol. 80, no. 4, p. 1673-1684. ISSN: 0924-090X.
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TOMÁŠEK, P. Asymptotic stability of a full term linear difference equation with two parameters. Tatra Mountains Mathematical Publications, 2015, vol. 63, no. 1, p. 283-290. ISSN: 1210-3195.
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BEREZANSKY, L.; DIBLÍK, J.; SVOBODA, Z.; ŠMARDA, Z. Simple uniform exponential stability conditions for a system of linear delay differential equations. APPLIED MATHEMATICS AND COMPUTATION, 2015, vol. 2015, no. 250, p. 605-614. ISSN: 0096-3003.
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BATTELLI, F.; DIBLÍK, J.; FEČKAN, M.; PICKTON, J.; POSPÍŠIL, M.; SUSANTO, H. Dynamics of generalized PT-symmetric dimers with time-periodic gain–loss. NONLINEAR DYNAMICS, 2015, vol. 81, no. 1, p. 353-371. ISSN: 0924-090X.
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ČERMÁK, J.; JÁNSKÝ, J.; TOMÁŠEK, P. Two types of stability conditions for linear delay difference equations. Applicable Analysis and Discrete Mathematics, 2015, vol. 9, no. 4, p. 120-138. ISSN: 1452-8630.
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NECHVÁTAL, L. On asymptotics of discrete Mittag-Leffler function. Mathematica Bohemica, 2014, vol. 139, no. 4, p. 667-675. ISSN: 0862-7959.
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DIBLÍK, J. A note on explicit criteria for the existence of positive solutions to the linear advanced equation \dot (t) = c(t)x(t + \tau). APPLIED MATHEMATICS LETTERS, 2014, vol. 35, no. 2014, p. 72-76. ISSN: 0893-9659.
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DIBLÍK, J.; KÚDELČÍKOVÁ, M.; JANGLAJEW, K. An explicit coefficient criterion for the existence of positive solutions to the linear advanced equation. DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES B, 2014, vol. 19, no. 2014, p. 2461-2467. ISSN: 1531-3492.
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ČERMÁK, J.; KISELA, T. Introduction to Stability Theory of Linear Fractional Difference Equations. In Fractional Calculus: Theory. Mathematics Research Developments. 2014. p. 117-162. ISBN: 978-1-63463-002-3.
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ČERMÁK, J.; JÁNSKÝ, J. Explicit stability conditions for a linear trinomial delay difference equation. APPLIED MATHEMATICS LETTERS, 2015, vol. 43, no. 5, p. 56-60. ISSN: 0893-9659.
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ČERMÁK, J.; DRAŽKOVÁ, J. On stability sets for numerical discretizations of neutral delay differential equations. Tatra Mountains Mathematical Publications, 2015, vol. 63, no. 2, p. 89-100. ISSN: 1210-3195.
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ČERMÁK, J.; KISELA, T. Exact and discretized stability of the Bagley-Torvik equation. Journal of Computational and Applied Mathematics, 2014, vol. 269, no. 10, p. 53-67. ISSN: 0377-0427.
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ČERMÁK, J.; JÁNSKÝ, J. Stability switches in linear delay difference equations. APPLIED MATHEMATICS AND COMPUTATION, 2014, vol. 243, no. 9, p. 755-766. ISSN: 0096-3003.
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Responsibility: Došlá Zuzana, Prof. RNDr., DrSc.