Oscillation results for time scale symplectic systems

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Authors	ŠIMON HILSCHER Roman ZEIDAN Vera
Year of publication	2009
Type	Article in Proceedings
Conference	Proceedings of the 14th International Conference on Difference Equations and Applications
MU Faculty or unit	Faculty of Science
Citation
Field	General mathematics
Keywords	Time scale; Time scale symplectic system; Linear Hamiltonian system; Generalized focal point; Conjoined basis; Oscillation; Nonoscillation; Quadratic functional; Sturmian comparison theorem; Riccati equation
Description	In this paper we study oscillation and nonoscillation properties of symplectic dynamic systems over a time scale interval which is unbounded above. We derive Sturmian-type comparison theorems and characterizations of the definiteness of the associated quadratic functional. These results extend recent ones for the bounded time scale domain, and they are also new for the special case of the discrete symplectic systems.
Related projects:	Mathematical structures and their physical applications Asymptotika, oscilace a kvadratické funkcionály v teorii dynamických rovnic Difference equations and dynamic equations on time scales II Second order optimality conditions for optimization problems