Project detail

# Diferenční rovnice a dynamické rovnice na "time scales" III.

Duration: 01.01.2010 — 31.12.2014

Mark

GAP201/10/1032

Default language

Czech

People responsible

Diblík Josef, prof. RNDr., DrSc.
- principal person responsible (2010-01-01 - not assigned)

Units

Department of Mathematics
- (2010-01-01 - not assigned)

Funding resources

Czech Science Foundation - Standardní projekty

- whole funder (2010-01-01 - 2014-12-31)

Results

HLAVIČKOVÁ, I. Finding initial data generating bounded solutions of difference equations. In XXVIII. International Colloquium on the Management of Educational Process. Brno: UNOB Brno, 2010. p. 74-81. ISBN: 978-80-7231-733-2.
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HLAVIČKOVÁ, I. Bisection method for finding initial data generating bounded solutions of discrete equations. In Proceedings of the 9th International Conference APLIMAT 2010. Bratislava: 2010. p. 191-198. ISBN: 978-80-89313-47-1.
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DIBLÍK, J.; BAŠTINEC, J.; BAŠTINCOVÁ, A. Oscillation of solution of a linear third-order discrete delayed equation. In 10th International conference APLIMAT. Bratislava: FME STU, 2011. p. 199-205. ISBN: 978-80-89313-51-8.
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VÍTOVEC, J.; ŘEHÁK, P. Regularly varying decreasing solutions of half-linear dynamic equations. In Discrete Dynamics and Difference Equations, Proceedings of the Twelfth International Conference on Difference Equations and Applications. 2010. p. 375-382. ISBN: 978-981-4287-64-7.
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DIBLÍK, J.; MORÁVKOVÁ, B. A note on a representation of solutions of impulsive linear discrete systems with constant coefficients and a single delay. In 10th International conference APLIMAT. Bratislava: FME STU, 2011. p. 231-236. ISBN: 978-80-89313-51-8.
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HLAVIČKOVÁ, I. How to find a bounded solution of the discrete analogue of the Emden-Fowler equation. In Proceedings of the 10th International Conference APLIMAT 2011. Bratislava: 2011. p. 281-286. ISBN: 978-80-89313-51-8.
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BAŠTINEC, J.; PIDDUBNA, G. Controllability of stationary linear systems with delay. In 10th International conference APLIMAT. Bratislava: FME STU, 2011. p. 207-216. ISBN: 978-80-89313-51-8.
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VÍTOVEC, J.; ŘEHÁK, P. q-Karamata functions and second order q-difference equations. Electronic Journal of Qualitative Theory of Differential Equations, 2011, vol. 24 (2011), no. 4, p. 1-20. ISSN: 1417-3875.
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HLAVIČKOVÁ, I. Bisection Method for Finding Initial Data Generating Bounded Solutions of Discrete Equations II. Journal of Applied Mathematics, 2010, vol. III, no. 2, p. 99-106. ISSN: 1337-6365.
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DIBLÍK, J.; ŠMARDA, Z.; KHUSAINOV, D.; GRYTSAY, I. Stability of Nonlinear Autonomous Quadratic Discrete Systems in the Critical Case. DISCRETE DYNAMICS IN NATURE AND SOCIETY, 2010, vol. 2010, no. Article ID 53908, p. 1-23. ISSN: 1026-0226.
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DIBLÍK, J.; MORÁVKOVÁ, B. Representation of Solutions of Linear Discrete Systems with Constant Coefficients, a Single Delay and with Impulses. Journal of Applied Mathematics, 2010, vol. III.(2010), no. 2, p. 45-52. ISSN: 1337-6365.
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DIBLÍK, J.; ŠMARDA, Z.; BAŠTINEC, J. Oscillation of solutions of a linear second-order discrete delayed equation. Advances in Difference Equations, 2010, vol. 2010, no. 2010, p. 1-11. ISSN: 1687-1839.
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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.; BAŠTINEC, J.; KHUSAINOV, D.; BAŠTINCOVÁ, A. Exponential stability and estimation of solutions of linear differential systems of neutral type with constant coefificients. Boundary Value Problems, 2010, vol. 2010, no. 1, p. 1-20. ISSN: 1687-2762.
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VÍTOVEC, J. Theory of rapid variation on time scales with applications to dynamic equations. Archivum Mathematicum, 2010, vol. 46 (2010), no. 4, p. 263-284. ISSN: 1212-5059.
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DIBLÍK, J.; BEREZANSKY, L.; BAŠTINEC, J.; ŠMARDA, Z. On the Critical Case in Oscillation for Differential Equations with a Single Delay and with Several Delays. Abstract and Applied Analysis, 2010, vol. 2010, no. Article ID 41789, p. 1-20. ISSN: 1085-3375.
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DIBLÍK, J.; BAŠTINCOVÁ, A.; BAŠTINEC, J.; KHUSAINOV, D.; SHATYRKO, A. Estimates of perturbed nonlinear systems of indirect control of neutral type. Cybernetics and computer enginering, 2010, roč. 2010, č. 160, s. 72-85. ISSN: 0452-9901.
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VÍTOVEC, J. Theory of regularly and rapidly varying functions on time scales and its application to dynamic equations. Muni PRESS. Muni PRESS. Brno: Masaryk University, 2011. 90 p. ISBN: 978-80-210-5426-4.
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FUCHS, P.; NOVÁK, M.; VÍTOVEC, J. The four-element Windkessel model analysis in MapleSim. In Proceedings EDS '11 IMAPS CS International Conference Brno, Czech Republic, June 22-23, 2011. Brno: Vysoké učení technické v Brně, 2012. p. 18-24. ISBN: 978-80-214-4303-7.
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VÍTOVEC, J. Positive decreasing solutions of half-linear dynamic equations. In XXIX International Colloquium on the Management of the Educational Process. Proceedings. Brno: Univerzita obrany, 2011. p. 1-9. ISBN: 978-80-7231-779-0.
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HLAVIČKOVÁ, I. How to find initial data generating bounded solutions of discrete equations. Tatra Mountains Mathematical Publications, 2011, vol. 2011, no. 48, p. 83-90. ISSN: 1210-3195.
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DIBLÍK, J.; HLAVIČKOVÁ, I. Asymptotic behavior of solutions of delayed difference equations. Abstract and Applied Analysis, 2011, vol. 2011, no. Article ID 67196, p. 1-24. ISSN: 1085-3375.
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DIBLÍK, J.; MORÁVKOVÁ, B. Representation of solutions of impulsive linear discrete systems with constant coefficients and a single delay. In XXIX International Colloquium on the Management of Educational Process. Brno: 2011. p. 1-6. ISBN: 978-80-7231-779-0.
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DIBLÍK, J.; HALFAROVÁ, H. Discrete systems of linear equations with weak delay. In XXIX International Colloquium on the Management of Educational Process. Brno: 2011. p. 1-4. ISBN: 978-80-7231-779-0.
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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.; RŮŽIČKOVÁ, M.; SCHMEIDEL, E.; ZBASZYNIAK, M. Weighted asymptotically periodic solutions of linear volterra difference equations. Abstract and Applied Analysis, 2011, vol. 2011, no. 1, p. 1-14. ISSN: 1085-3375.
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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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BAŠTINEC, J.; DZHALLADOVA, I. Sufficient conditions for stability of solutions of systems of nonlinear differential equations with right-hand side depending on Markov's process. In 7. konference o matematice a fyzice na vysokých školách technických s mezinárodní účastí. 2011. p. 23-29. ISBN: 978-80-7231-815-5.
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BAŠTINEC, J.; PIDDUBNA, G. Solution of Matrix Linear Delayed System. In 7. konference o matematice a fyzice na vysokých školách technických s mezinárodní účastí. 2011. p. 48-57. ISBN: 978-80-7231-815-5.
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BAŠTINEC, J.; PIDDUBNA, G. Solution of Matrix Linear Delayed System. In XXIX International Colloquium on the Management on the Educational Process aimed at current issues in science, educatio and creative thinking development. 2011. p. 51-60. ISBN: 978-80-7231-780-6.
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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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BAŠTINEC, J.; PIDDUBNA, G. Stability of a certain class of matrix differential delayed equation. In International Conference PRESENTATION of MATHEMATICS 11, Proceedings. Liberec: Technical University of Liberec, 2011. p. 7-14. ISBN: 978-80-7372-773-4.
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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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DIBLÍK, J.; RŮŽIČKOVÁ, M.; ŠMARDA, Z.; ŠUTÁ, Z. Asymptotic convergence of the solutions of a dynamic equation on discrete time scales. Abstract and Applied Analysis, 2012, vol. 2012, no. ID 580750, p. 1-20. ISSN: 1085-3375.
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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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BAŠTINEC, J.; PIDDUBNA, G. Solutions and stability of solutions of a linear diffeential matrix system with delay. In Proceedings of the 2nd International Conference on Mathematical Models for Engineering Science (MMES II). 2011. p. 94-99. ISBN: 978-1-61804-055-8.
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BAŠTINEC, J.; PIDDUBNA, G. Solutions and stability of solutions of a linear diffeential matrix system with delay. In Proceedings of The IEEEAM/NAUN International Conferences. 2011. p. 94-99. ISBN: 978-1-61804-058-9.
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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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BAŠTINEC, J.; PIDDUBNA, G. CONTROLLABILITY FOR A CERTAIN CLASS OF LINEAR MATRIX SYSTEMS WITH DELAY. In APLIMAT, 11th International Conference. Bratislava: STU, 2012. p. 93-102. ISBN: 978-80-89313-58-7.
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DIBLÍK, J.; SCHMEIDEL, E. On the existence of solutions of linear Volterra difference equations asymptotically equivalent to a given sequence. APPLIED MATHEMATICS AND COMPUTATION, 2012, vol. 2012, no. 18, p. 9310-9320. ISSN: 0096-3003.
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BAŠTINEC, J.; PIDDUBNA, G. Controllability and control construction of linear matrix system with delay. In XIV International Scientific Conference Devoted to the memory of Academician M. Kravchuk. Kyev, Ukraina: Kyev University, 2012. p. 11-12. ISBN: 978-617-696-013-3.
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DIBLÍK, J.; HLAVIČKOVÁ, I. Asymptotic upper and lower estimates of a class of positive solutions of a discrete linear equation with a single delay. Abstract and Applied Analysis, 2012, vol. 2012, no. ArticleID 764351, p. 1-12. ISSN: 1085-3375.
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PIDDUBNA, G.; BAŠTINEC, J. Solution of one Practice Matrix Linear Delayed System. In XXX International Colloquium on the Management of Educational Process, Proceedings of abstracts and electronic version of reviewed contributions on CD-ROM. Brno: UNOB, 2012. p. 48-48. ISBN: 978-80-7231-865-0.
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DIBLÍK, J.; BAŠTINEC, J.; KHUSAINOV, D.; BAŠTINCOVÁ, A. Interval stability of linear systems of neural type. Žurnal občisljuvalnoji ta prikladnoji matematiki, 2012, vol. 2011, no. 391060, p. 148-160. ISSN: 0868-6912.
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STEVIČ, S.; DIBLÍK, J.; IRIČANIN, B.; ŠMARDA, Z. On a Third-Order System of Difference Equations with Variable Coefficients. Abstract and Applied Analysis, 2012, vol. 2012, no. Article ID 50852, p. 1-22. ISSN: 1085-3375.
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DIBLÍK, J.; HLAVIČKOVÁ, I. Asymptotic upper and lower estimates of solutions of a class of discrete linear equations with a single delay. Abstracts CDDEA 2012. Žilina: University of Žilina, 2012. p. 14-15. ISBN: 978-80-554-0543-8.
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STEVIČ, S.; DIBLÍK, J.; IRIČANIN, B.; ŠMARDA, Z. On a Periodic System of Difference Equations. Abstract and Applied Analysis, 2012, vol. 2012, no. Article ID 25871, p. 1-5. ISSN: 1085-3375.
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STEVIČ, S.; DIBLÍK, J.; IRIČANIN, B.; ŠMARDA, Z. On the Difference Equation $x_{n+1} =x_n x_{n-k}/x_{n-k+1} (a+bx_n x_{n-k})$. Abstract and Applied Analysis, 2012, vol. 2012, no. Article ID 10804, p. 1-9. ISSN: 1085-3375.
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STEVIČ, S.; DIBLÍK, J.; IRIČANIN, B.; ŠMARDA, Z. On the Difference Equation $x_n = a _nx_{n-k}/(b_nc_n x_{n-1} ... x_{n-k})$. Abstract and Applied Analysis, 2012, vol. 2012, no. ID 409237, p. 1-20. ISSN: 1085-3375.
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VÍTOVEC, J. SOME GENERALIZATIONS IN THEORY OF RAPID VARIATION ON TIME SCALES AND ITS APPLICATION IN DYNAMIC EQUATIONS. In Aplimat 2012. 2012. p. 213-220. ISBN: 978-80-89313-58-7.
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PIDDUBNA, G.; BAŠTINEC, J.; KHUSAINOV, D. Representation of solutions for linear stationary systems with one delay. In Functional Differential Equations and Applications 2012. Functional Differential Equations. Ariel: AUCS, 2012. p. 20-21. ISSN: 0793-1786.
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PIDDUBNA, G.; BAŠTINEC, J. Solution of one practice matrix linear delayed system. In XXX International Colloquium on the Management of Educational Process. Brno: UNOB, 2012. p. 33-38. ISBN: 978-80-7231-866-7.
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PIDDUBNA, G.; BAŠTINEC, J. Controllability of matrix linear differential systems with delay. In Conference on Differential and Difference Equations and Applications, 2012. Žilina: UZ, 2012. p. 36-36. ISBN: 978-80-554-0543-8.
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PIDDUBNA, G.; BAŠTINEC, J. Controllability research of linear differential matrix system with delay. In Modelling, Control and Stability MCS-2012. Simferopol: DIAIP, 2012. p. 24-25. ISBN: 978-966-491-327-7.
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DIBLÍK, J.; RŮŽIČKOVÁ, M.; ŠUTÁ, Z. Asymptotic convergence of the solutions of a discrete system with delays. APPLIED MATHEMATICS AND COMPUTATION, 2012, vol. 2012, no. 18, p. 4036-4044. ISSN: 0096-3003.
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DIBLÍK, J.; VÍTOVEC, J. Bounded solutions of delay dynamic equations on time scales. Advances in Difference Equations, 2012, vol. 2012, no. 1, p. 1-9. ISSN: 1687-1847.
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BEREZANSKY, L.; BAŠTINEC, J.; DIBLÍK, J.; ŠMARDA, Z. On a delay population model with quadratic nonlinearity. Advances in Difference Equations, 2012, vol. 2012, no. 1, p. 1-13. ISSN: 1687-1847.
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BAŠTINEC, J.; PIDDUBNA, G. Controllability for a certain class of linear matrix systems with delay. Journal of Applied Mathematics, 2013, vol. V(2012), no. II, p. 13-23. ISSN: 1337-6365.
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VÍTOVEC, J. Some generalizations in theory of rapid variation on time scales and its applications in dynamic equations. Journal of Applied Mathematics, 2013, vol. 5 (2012), no. 2, p. 139-146. ISSN: 1337-6365.
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DIBLÍK, J.; IRIČANIN, B.; STEVIČ, S.; ŠMARDA, Z. On Some Symmetric Systems of Difference Equations. Abstract and Applied Analysis, 2013, vol. 2013, no. Article ID 2467, p. 1-7. ISSN: 1085-3375.
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DIBLÍK, J.; BAŠTINEC, J. Existence of a positive solution of discrete equations of (k+1) order. In ISAAC, 9th congres, Krakow 2013. Krakow: 2013. p. 29-30. ISBN: 978-83-62652-52-5.
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POSPÍŠIL, M.; DIBLÍK, J.; FEČKAN, M. Observability of difference equations with a delay. In 11th International Conference on Numerical Analysis and Applied Mathematics: ICNAAM 2013. AIP conference proceedings. Melville, New York: American Institute of Physics, 2013. p. 478-481. ISBN: 978-0-7354-1184-5. ISSN: 0094-243X.
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DIBLÍK, J.; VÍTOVEC, J. Lower and upper estimates of solutions to systems of delay dynamic equations on time scales. Boundary Value Problems, 2013, vol. 2013, no. 1, p. 1-14. ISSN: 1687-2770.
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DIBLÍK, J.; VÍTOVEC, J. Asymptotic behavior of solutions of systems of dynamic equations on time scales in a set whose boundary is a combination of strict egress and strict ingress points. APPLIED MATHEMATICS AND COMPUTATION, 2014, vol. 238, no. 6, p. 289-299. ISSN: 0096-3003.
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DIBLÍK, J.; MORÁVKOVÁ, B. Representation of the solutions of linear discrete systems with constant coefficients and two delays. Abstract and Applied Analysis, 2014, vol. 2014, no. 1, p. 1-19. ISSN: 1085-3375.
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DIBLÍK, J.; HALFAROVÁ, H. General explicit solution of planar weakly delayed linear discrete systems and pasting its solutions. Abstract and Applied Analysis, 2014, vol. 2013, no. 1, p. 1-37. ISSN: 1085-3375.
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STEVIČ, S.; DIBLÍK, J.; IRIČANIN, B.; ŠMARDA, Z. On a solvable system of rational difference equations. JOURNAL OF DIFFERENCE EQUATIONS AND APPLICATIONS, 2014, vol. 2014(20), no. 5-6, p. 811-825. ISSN: 1023-6198.
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VÍTOVEC, J. Critical oscillation constant for Euler-type dynamic equations on time scales. APPLIED MATHEMATICS AND COMPUTATION, 2014, vol. 243, no. 7, p. 838-848. ISSN: 0096-3003.
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DIBLÍK, J.; FEČKAN, M.; POSPÍŠIL, M. On the new control functions for linear discrete delay systems. SIAM JOURNAL ON CONTROL AND OPTIMIZATION, 2014, vol. 65, no. 1, p. 1745-1760. ISSN: 0363-0129.
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DIBLÍK, J.; STAVROULAKIS, I.; CHATZARAKIS, G.; MILIARAS, G. Classification of neutral difference equations of any order with respect to the asymptotic behavior of their solutions. APPLIED MATHEMATICS AND COMPUTATION, 2014, vol. 2014, no. 227, p. 77-90. ISSN: 0096-3003.
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HASIL, P.; VÍTOVEC, J. Conditional oscillation of half-linear Euler-type dynamic equations on time scales. Electronic Journal of Qualitative Theory of Differential Equations, 2015, vol. 2015, no. 6, p. 1-24. ISSN: 1417-3875.
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POSPÍŠIL, M.; DIBLÍK, J.; FEČKAN, M. On relative controllability of delayed difference equations with multiple control functions. In Proceedings of the International Conference on Numerical Analysis and Applied Mathematics 2014 (ICNAAM-2014). AIP conference proceedings. Melville, New York: American Institute of Physics, 2015. p. 130001-1 (130001-4 p.)ISBN: 978-0-7354-1287-3. ISSN: 0094-243X.
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HLAVIČKOVÁ, I. An application of Markov chains in digital communication. Tatra Mountains Mathematical Publications, 2015, no. 63, p. 129-137. ISSN: 1210-3195.
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