Czech Science Foundation - Standardní projekty

- whole funder (2011-01-01 - 2015-12-31)

GAP201/11/0768

Czech

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

Institute of Mathematics
- (2011-01-01 - 2015-12-31)

DIBLÍK, J.; BAŠTINEC, J.; ŠMARDA, Z. Oscilation and nonoscilation of solution of differential equation with delay. In Dynamical System Modelling and Stability Investigation. Kyjev, Ukrajina: University of Kyiv, UA, 2011. p. 25-26. ISBN: 9667652009.
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DIBLÍK, J.; ŠMARDA, Z.; SVOBODA, Z.; KHUSAINOV, D. Instable trivial solution of autonomous differential systems with quadratic right-hand sides in a cone. Abstract and Applied Analysis, 2011, vol. 2011, no. Article ID 15491, p. 1-23. ISSN: 1085-3375.
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DIBLÍK, J.; ZAFER, A. On stability of linear delay differential equations under Perron's condition. Abstract and Applied Analysis, 2011, vol. 2011, no. 1, p. 1-9. ISSN: 1085-3375.
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ČERMÁK, J.; KISELA, T.; NECHVÁTAL, L. Discrete Mittag-Leffler functions in linear fractional difference equations. Abstract and Applied Analysis, 2011, vol. 2011, no. 2011, p. 1-21. ISSN: 1085-3375.
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BOICHUK, A.; DIBLÍK, J.; KHUSAINOV, D.; RŮŽIČKOVÁ, M. Boundary-value problems for weakly nonlinear delay differential systems. Abstract and Applied Analysis, 2011, vol. 2011, no. 1, p. 1-19. ISSN: 1085-3375.
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DZHALLADOVA, I.; BAŠTINEC, J.; DIBLÍK, J.; KHUSAINOV, D. Estimates of exponential stability for solutions of stochastic control systems with delay. Abstract and Applied Analysis, 2011, vol. 2011, no. 1, p. 1-14. ISSN: 1085-3375.
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DIBLÍK, J.; NOWAK, C. Compatible and incompatible nonuniqueness conditions for the classical Cauchy problem. Abstract and Applied Analysis, 2011, vol. 2011, no. 1, p. 1-15. ISSN: 1085-3375.
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DIBLÍK, J.; KHUSAINOV, D. Representation of solution of the first boundary value problem for delay systems. Bulletin Kiev University, series: physics and Mathematics, 2011, vol. 2011, no. 1, p. 59-62. ISSN: 1812-5409.
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BAŠTINEC, J.; BEREZANSKY, L.; DIBLÍK, J.; ŠMARDA, Z. A final result on the oscillation of solutions of the linear discrete delayed equation \Delta x(n)=-p(n)x(n-k) with a positive coefficient. Abstract and Applied Analysis, 2011, vol. vol. 2011, no. Article ID 58632, p. 1-28. ISSN: 1085-3375.
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DIBLÍK, J.; BAŠTINCOVÁ, A.; BAŠTINEC, J. Oscillation of solution of a linear third-order discrete delayed equation. In NINTH INTERNATIONAL CONFERENCE ON SOFT COMPUTING APPLIED IN COMPUTER AND ECONOMIC ENVIRONMENTS, ICSC 2011. Kunovice: EPI, 2011. p. 95-101. ISBN: 978-80-7314-221-6.
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DIBLÍK, J.; ŠMARDA, Z.; BAŠTINEC, J.; BEREZANSKY, L. Oscillation of solutions of the linear discrete delayed equation and related problems. In Proceedings 2011 World Congress on Engineering and Technology. Shanghai Čína: 2011. p. 457-461. ISBN: 978-1-61284-363-6.
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BAŠTINEC, J.; DIBLÍK, J.; ŠMARDA, Z. An explicit criterion for the existence of positive solutions of the linear delayed equation $\dot x(t)=-c(t)x(t-\tau(t))$. Abstract and Applied Analysis, 2011, vol. 2011, no. 11, p. 1-10. ISSN: 1085-3375.
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DIBLÍK, J.; KHUSAINOV, D.; RŮŽIČKOVÁ, M.; BAŠTINCOVÁ, A. On a dynamical model with delay for the economy. Nonlinear Oscillations, 2011, vol. 14920110, no. 4, p. 556-568. ISSN: 1536-0059.
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SVOBODA, Z. Asymptotic properties of system of the delayed linear differential equations of special type. In Dynamical System Modelling and Stability Investigation Abstracts of Conference Reports. Kyjev: 2011. p. 156-157. ISBN: 9667652009.
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DIBLÍK, J.; KUKHARENKO, O.; MORÁVKOVÁ, B.; KHUSAINOV, D. Delayed exponential functions and their application to representations of solutions of linear equations with constant coefficients and with single delay. In Proceedings of the IEEEAM/NAUN International Conferences. 2011. p. 82-87. ISBN: 978-1-61804-058-9.
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HRABALOVÁ, J. On stability intervals of Euler methods for a delay differential equation. Journal of Applied Mathematics, 2013, vol. 5, no. 2, p. 77-84. ISSN: 1337-6365.
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ČERMÁK, J.; DVOŘÁKOVÁ, S. Boundedness and asymptotic properties of solutions of some linear and sublinear delay difference equations. APPLIED MATHEMATICS LETTERS, 2012, vol. 25, no. 2, p. 813-817. ISSN: 0893-9659.
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ČERMÁK, J.; JÁNSKÝ, J.; TOMÁŠEK, P. On necessary and sufficient conditions for the asymptotic stability of higher order linear difference equations. JOURNAL OF DIFFERENCE EQUATIONS AND APPLICATIONS, 2012, vol. 18, no. 11, p. 1781-1800. ISSN: 1023-6198.
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HRABALOVÁ, J. On stability intervals of Euler methods for a delay differential equation. In APLIMAT 11th INTERNATIONAL CONFERENCE. Bratislava: Aplimat, 2012. p. 153-160. ISBN: 978-80-89313-58-7.
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DIBLÍK, J.; KHUSAINOV, D.; KUKHARENKO, O.; SVOBODA, Z. Solution of the first boundary-value problem for a system of autonomous second-order linear partial differential equations of parabolic type with a single delay. Abstract and Applied Analysis, 2012, vol. 2012, no. Article ID 21904, p. 1-27. ISSN: 1085-3375.
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ČERMÁK, J.; KISELA, T.; NECHVÁTAL, L. Stability and asymptotic properties of a linear fractional difference equation. Advances in Difference Equations, 2012, vol. 2012, no. 1, p. 1-14. ISSN: 1687-1847.
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BAŠTINEC, J.; DIBLÍK, J.; HALFAROVÁ, H.; ŠMARDA, Z. An explicit criterion for the existence of positive solutions of the linear delayed equation. In Modelling, Control and Stability MCS-2012. Krym, Simferopol: 2012. p. 26-27. ISBN: 978-966-491-327-7.
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KHAN, Y.; SVOBODA, Z.; ŠMARDA, Z. Solving certain classes of Lane-Emden type equations using differential transformation method. Advances in Difference Equations, 2012, vol. 2012, no. 1, p. 1-13. ISSN: 1687-1847.
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DIBLÍK, J.; DZHALLADOVA, I.; RŮŽIČKOVÁ, M. The stability of nonlinear differential systems with random parameters. Abstract and Applied Analysis, 2012, vol. 2012, no. Article ID924107, p. 1-27. ISSN: 1085-3375.
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STEVIČ, S.; DIBLÍK, J.; IRIČANIN, B.; ŠMARDA, Z. On Some Solvable Difference Equations and Systems of Difference Equations. Abstract and Applied Analysis, 2012, vol. 2012, no. ID 541761, p. 1-11. ISSN: 1085-3375.
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KHAN, Y.; DIBLÍK, J.; FARAZ, N.; ŠMARDA, Z. An efficient new perturbative Laplace method for space-time fractional telegraph equations. Advances in Difference Equations, 2012, vol. 2012, no. 1, p. 1-11. ISSN: 1687-1847.
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ČERMÁK, J.; KISELA, T.; NECHVÁTAL, L. Stability regions for linear fractional differential systems and their discretizations. APPLIED MATHEMATICS AND COMPUTATION, 2013, vol. 219, no. 12, p. 7012-7022. ISSN: 0096-3003.
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ŠMARDA, Z.; KHAN, Y. Singular Initial Value Problem for a System of Integro-Differential Equations. Abstract and Applied Analysis, 2012, vol. 2012, no. ID 918281, p. 1-18. ISSN: 1085-3375.
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SVOBODA, Z.; DIBLÍK, J.; KHUSAINOV, D. SOME PROPERTIES OF SPECIAL DELAYED MATRIX FUNCTIONS IN THEORY OF SYSTEMS OF LINEAR DIFFERENTIAL EQUATIONS WITH CONSTANT COEFFICIENTS AND WITH SINGLE DELAY. In 11-th Intenational conference APLIMAT 12. Bratislava: STU, 2012. p. 205-212. ISBN: 978-80-89313-58-7.
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SVOBODA, Z. Asymptotic properties of delayed matrix functions. In Modelling, Control and Stability MCS-2012. Krym, Simferopol: 2012. p. 40-42. ISBN: 978-966-491-327-7.
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SHATYRKO, A.; DIBLÍK, J.; KHUSAINOV, D.; RŮŽIČKOVÁ, M. Stabilization of Lure-type Nonlinear Control Systems by Lyapunov-Krasovskii Functionals. Advances in Difference Equations, 2012, vol. 2012, no. 1, p. 1-11. ISSN: 1687-1847.
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ČERMÁK, J.; TOMÁŠEK, P. On delay-dependent stability conditions for a three-term linear difference equation. Funkcialaj Ekvacioj Serio Internacia, 2014, vol. 57, no. 1, p. 91-106. ISSN: 0532-8721.
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HRABALOVÁ, J. Stability properties of a discretized neutral delay differential equation. Tatra Mountains Mathematical Publications, 2013, vol. 2013, no. 54, p. 83-92. ISSN: 1210-3195.
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HRABALOVÁ, J.; TOMÁŠEK, P. On stability regions of the modified midpoint method for a linear delay differential equation. Advances in Difference Equations, 2013, vol. 2013, no. 177, p. 1-10. ISSN: 1687-1847.
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TOMÁŠEK, P. An asymptotic estimate for linear delay differential equations with power delayed arguments. Advances in Dynamical Systems and Applications (ADSA), 2013, vol. 8, no. 2, p. 379-386. ISSN: 0973-5321.
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DIBLÍK, J.; KUDELČÍKOVÁ, M. Positive solutions of advanced differential systems. The Scientific World Journal, 2013, vol. 2013, no. Article ID, p. 1-8. ISSN: 1537-744X.
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ČERMÁK, J. Some qualitative properties of linear dynamic equations with multiple delays. Advances in Difference Equations, 2013, vol. 2013, no. 2013, p. 1-12. ISSN: 1687-1847.
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ČERMÁK, J.; DRAŽKOVÁ, J. On stability regions for some delay differential equations and their discretizations. Periodica Mathematica Hungarica, 2014, vol. 68, no. 2, p. 193-206. ISSN: 0031-5303.
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ČERMÁK, J.; JÁNSKÝ, J. On a generalization of the Levin-May Theorem. Carpathian Journal of Mathematics, 2014, vol. 30, no. 1, p. 55-62. ISSN: 1584-2851.
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DIBLÍK, J.; FEČKAN, M.; POSPÍŠIL, M. Forced Fermi-Pasta-Ulam lattice maps. Miskolc Mathematical Notes, 2013, vol. 14, no. 1, p. 63-78. ISSN: 1787-2405.
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DIBLÍK, J.; FEČKAN, M.; POSPÍŠIL, M. Representation of a solution of the Cauchy problem for an oscillating system with two delays and permutable matrices. Ukrainian Mathematical, 2013, vol. 65, no. 1, p. 64-76. ISSN: 0041-5995.
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DIBLÍK, J.; FEČKAN, M.; POSPÍŠIL, M. Representation of a solution of the Cauchy problem for an oscillating system with multiple delays and pairwise permutable matrices. Abstract and Applied Analysis, 2013, vol. 2013, no. 1, p. 1-10. ISSN: 1085-3375.
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DIBLÍK, J.; REBENDA, J.; ŠMARDA, Z. Singular Initial Value Problem for Certain Classes of Systems of Ordinary Differential Equations. Abstract and Applied Analysis, 2013, vol. 2013, no. 1, p. 1-12. ISSN: 1085-3375.
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DIBLÍK, J.; DZHALLADOVA, I.; MICHALKOVÁ, M.; RŮŽIČKOVÁ, M. Modeling of applied problems by stochastic systems and their analysis using the moment equations. Advances in Difference Equations, 2013, vol. 2013, no. 1, p. 1-12. ISSN: 1687-1847.
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DIBLÍK, J.; DZHALLADOVA, I.; MICHALKOVÁ, M.; RŮŽIČKOVÁ, M. Moment equations in modeling a stable foreign currency exchange market in conditions of uncertainty. Abstract and Applied Analysis, 2013, vol. 2013, no. 1, p. 1-12. ISSN: 1085-3375.
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DIBLÍK, J.; RŮŽIČKOVÁ, M.; CHUPÁČ, R. Unbounded solutions of the equation $\dot y(t)=\sum_{i=1}^{n}\beta_{i}$ (t)\left[y(t-\delta_{i})-y(t-\tau_{i})\right]$. APPLIED MATHEMATICS AND COMPUTATION, 2013, vol. 2013, no. 221, p. 610-619. ISSN: 0096-3003.
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ČERMÁK, J.; HRABALOVÁ, J. Delay-dependent stability criteria for neutral delay differential and difference equations. DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS, 2014, vol. 34, no. 11, p. 4577-4588. ISSN: 1078-0947.
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DIBLÍK, J.; FEČKAN, M.; POSPÍŠIL, M.; ROTHOS, V.; SUSANTO, H. Travelling waves in nonlinear magnetic metamaterials. In Localized Excitations in Nonlinear Complex Systems. Nonlinear Systems and Complexity. 2014. p. 335-358. ISBN: 978-3-319-02056-3.
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DIBLÍK, J.; IRIČANIN, B.; STEVIČ, S.; ŠMARDA, Z. Note on the existence of periodic solutions of a class of systems of differential-difference equations. APPLIED MATHEMATICS AND COMPUTATION, 2014, vol. 2014, no. 232, p. 922-928. ISSN: 0096-3003.
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STEVIČ, S.; DIBLÍK, J.; ŠMARDA, Z. On periodic and solutions converging to zero of some systems of differential-difference equations. APPLIED MATHEMATICS AND COMPUTATION, 2014, vol. 2014, no. 227, p. 43-49. ISSN: 0096-3003.
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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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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.; 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.; 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.; 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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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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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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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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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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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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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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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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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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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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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.; 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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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.; 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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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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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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