Project information
Linear Hamiltonian dynamic systems and half-linear dynamic equations
- Project Identification
- KJB1019407
- Project Period
- 1/2004 - 12/2006
- Investor / Pogramme / Project type
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Academy of Sciences of the Czech Republic
- The research grant projects for juniors
- MU Faculty or unit
- Faculty of Science
- Keywords
- linear Hamiltonian system, Riccati equation, quadratic functional, time scale, half-linear equation, oscillation, nonoscillation
The project is focused primarily on the investigation of the linear Hamiltonian dynamic systems on time scales and the half-linear dynamic equations on time scales. In particular, their qualitative properties will be studied and together with applications to control theory and calculus of variations. The investigation of the dynamic equations on time scales enables to obtain the results unifying the theories for the differential and difference equations, as well as for many other time scales, thus providing at the same time an explanation of the discrepancies between the continuous and discrete cases. The understanding of these discrepancies is important, for example, for numerical approximations. The main results will be presented at international meetings and published in international journals.
Publications
Total number of publications: 20
2006
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Function sequence technique for half-linear dynamic equations on time scales
Panamer. Math. J., year: 2006, volume: 16, edition: 1
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How the constants in Hille-Nehari theorems depend on time scales
Advances in Difference Equations, year: 2006, volume: 2006, edition: 1
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Implicit Riccati equations and quadratic functionals for discrete symplectic systems
International Journal of Difference Equations, year: 2006, volume: 1, edition: 1
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Riccati inequality and other results for discrete symplectic systems
Journal of Mathematical Analysis and Applications, year: 2006, volume: 322, edition: 2
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Time scale symplectic systems without normality
Journal of Differential Equations, year: 2006, volume: 230, edition: 1
2005
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Half-Linear Differential Equations
Year: 2005, number of pages: 517 s.
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Hardy inequality on time scales and its application to half-linear dynamic equations
J. Inequal. Appl., year: 2005, volume: 2005, edition: 5
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Necessary and sufficient conditions for oscillation of coupled nonlinear discrete systems
Difference Equations and Discrete Dynamical Systems, Proc. of 9th ICDEA, year: 2005
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Solvability of the discrete LQR-problem under minimal assumptions
Difference Equations and Discrete Dynamical Systems, year: 2005
2004
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Opial and Lypaunov type inequalities for half-linear dynamic equations
Dynamic Systems and Applications, year: 2004, volume: 13, edition: 3-4