Applications of time scale symplectic systems without normality

Warning

This publication doesn't include Faculty of Arts. It includes Faculty of Science. Official publication website can be found on muni.cz.

Authors	HILSCHER Roman ZEIDAN Vera
Year of publication	2008
Type	Article in Periodical
Magazine / Source	Journal of Mathematical Analysis and Applications
MU Faculty or unit	Faculty of Science
Citation
Field	General mathematics
Keywords	Time scale; Time scale symplectic system; Linear Hamiltonian system; Quadratic functional; Nonnegativity; Positivity; Conjoined
Description	Recently, the authors obtained new characterizations of the positivity and nonnegativity of a time scale quadratic functional F with separable endpoints related to a time scale symplectic system (S). In these results, the assumption of normality is absent. In this paper we present applications of such results. Namely, without assuming normality we derive Sturmian comparison theorems, results for general jointly varying endpoints, and characterizations of the positivity of F via the corresponding time scale Riccati equation, a certain perturbed quadratic functional, and a time scale Riccati inequality. These results generalize and unify many recent as well as classical ones.
Related projects:	Optimality conditions on time scales Difference Equations and Dynamic Equations on Time Scales. Mathematical structures and their physical applications Linear Hamiltonian dynamic systems and half-linear dynamic equations