Project information
Difference equations and dynamic equations on time scales II
- Project Identification
- GA201/07/0145
- Project Period
- 1/2007 - 12/2009
- Investor / Pogramme / Project type
-
Czech Science Foundation
- Standard Projects
- MU Faculty or unit
-
Faculty of Science
- prof. RNDr. Ondřej Došlý, DrSc.
- prof. RNDr. Zuzana Došlá, DSc.
- doc. Mgr. Petr Hasil, Ph.D.
- doc. Mgr. Zuzana Pátíková, Ph.D.
- Mgr. Šárka Pechancová, Ph.D.
- prof. RNDr. Zdeněk Pospíšil, Dr.
- Mgr. Viera Růžičková, Ph.D.
- Mgr. Pavel Řehák
- prof. RNDr. Roman Šimon Hilscher, DSc.
- doc. RNDr. Michal Veselý, Ph.D.
- Mgr. Jiří Vítovec, Ph.D.
- Keywords
- Symplectic system, quadratic functional, Riccati equation, half-linear equation, asymptotic theory, oscillatory properties
- Cooperating Organization
-
Mendel University in Brno
- Responsible person Mgr. Robert Mařík, PhD.
- Responsible person prof. RNDr. Josef Diblík, DrSc.
The project is a continuation of the project with the same title which started in 2004 and will be finished this year (project 201/04/0580 of GAČR). The research team is similar to the "old" project group and the main attention will be aimed to the directions where we achieved substantial results in the recent period. In particular, we will focus our attention to the following particular topics:
- qualitative theory of second order linear, half-linear, and quasilinear difference equations,
- symplectic difference systems and associated Riccati matrix equations with applications of obtained results in the theory of second order optimality conditions,
- asymptotic properties of solutions of linear and nonlinear difference systems, including delayed systems,
- symplectic dynamic systems on time scales, unifying theory of differential and diference systems,
- qualitative theory of second order dynamic equations on time scales.
Publications
Total number of publications: 55
2009
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On positivity of the three term 2n-order difference operators
Studies of the University of Žilina, Mathematical Series, year: 2009, volume: 23, edition: 1
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Oscillation results for time scale symplectic systems
Proceedings of the 14th International Conference on Difference Equations and Applications, year: 2009
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Perturbation principle in discrete half-linear oscillation theory
Stud. Univ. Žilina Math. Ser., year: 2009, volume: 23, edition: 4
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Picone type identities and definiteness of quadratic functionals on time scales
Applied Mathematics and Computation, year: 2009, volume: 215, edition: 7
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Rapidly varying decreasing solutions of half-linear difference equations
Mathematical and Computer Modelling, year: 2009, volume: 49, edition: 7-8, DOI
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Recessive solutions for half-linear dynamic equations
African Diaspora Journal of Mathematics, Special Issue in Memory of Prof. Ibni Oumar Mahamat Saleh, year: 2009, volume: 8 (2009), edition: 2
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Sturmian and spectral theory for discrete symplectic systems
Trans. Amer. Math. Soc., year: 2009, volume: 361, edition: 6
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Summation characterization of the recessive solution of half-linear difference equations
Adv. Difference Equ., year: 2009, volume: 2008, edition: ID 521058
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Trigonometric and hyperbolic systems on time scales
Dynamic Systems and Applications, year: 2009, volume: 18, edition: 3-4
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Weak maximum principle and accessory problem for control problems on time scales
Nonlinear Analysis, year: 2009, volume: 70, edition: 9