Applications of time scale symplectic systems without normality

• 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
• 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.

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