Project information
Optimality conditions on time scales
- Project Identification
- 1K04001
- Project Period
- 1/2004 - 8/2006
- Investor / Pogramme / Project type
-
Ministry of Education, Youth and Sports of the CR
- Programme of Support for Junior R&D Workers (National Research Programme)
- MU Faculty or unit
-
Faculty of Science
- prof. RNDr. Ondřej Došlý, DrSc.
- prof. RNDr. Roman Šimon Hilscher, DSc.
- Keywords
- Time scale, Quadratic functional, Variable endpoints, Conjugate and coupled point, Jacobi equation, Riccati equation, Nonnegativity, Positivity, Coercivity, Disconjugacy, Optimality conditions
The focus of this project is the study of 2nd order optimality conditions in
calculus of variations and optimal control problems on time scales.
These conditions are based on the nonnegativity (i.e. necessary optimality
conditions) and the positivity or coercivity (i.e. sufficient optimality
conditions) of the corresponding quadratic functionals of the second variation.
In particular, we will study their characterizations in terms of conjugate and
coupled points, and the solvability of the associated Jacobi and Riccati
dynamic equations.
Publications
Total number of publications: 11
2008
-
Applications of time scale symplectic systems without normality
Journal of Mathematical Analysis and Applications, year: 2008, volume: 340, edition: 1
-
Time scale embedding theorem and coercivity of quadratic functionals
Analysis (Munich), year: 2008, volume: 28, edition: 1
2007
-
Legendre, Jacobi, and Riccati type conditions for time scale variational problem with application
Dynamic Systems and Applications, year: 2007, volume: 16, edition: 3
-
Perturbation of nonnegative time scale quadratic functionals
Difference Equations, Special Functions, and Orthogonal Polynomials, year: 2007
2006
-
Comparison results for solutions of time scale matrix Riccati equations and inequalities
The Australian Journal of Mathematical Analysis and Applications, year: 2006, volume: 3, edition: 2
-
Coupled intervals for discrete symplectic systems
Linear Algebra and its Applications, year: 2006, volume: 419, edition: 2-3
-
Implicit Riccati equations and quadratic functionals for discrete symplectic systems
International Journal of Difference Equations, year: 2006, volume: 1, edition: 1
-
Riccati inequality and other results for discrete symplectic systems
Journal of Mathematical Analysis and Applications, year: 2006, volume: 322, edition: 2
-
Time scale symplectic systems without normality
Journal of Differential Equations, year: 2006, volume: 230, edition: 1
2005
-
Nonnegativity and positivity of quadratic functionals in the discrete calculus of variations: Survey
Journal of Difference Equations and Applications, year: 2005, volume: 11, edition: 9