Riccati inequality and other results for discrete symplectic systems

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Authors	HILSCHER Roman RŮŽIČKOVÁ Viera
Year of publication	2006
Type	Article in Periodical
Magazine / Source	Journal of Mathematical Analysis and Applications
MU Faculty or unit	Faculty of Science
Citation
Field	General mathematics
Keywords	Discrete symplectic system; Quadratic functional; Nonnegativity; Positivity; Riccati inequality; Riccati equation; Conjoined basis; Sturmian theorem
Description	In this paper we establish several new results regarding the positivity and nonnegativity of discrete quadratic functionals F associated with discrete symplectic systems. In particular, we derive (i) the Riccati inequality for the positivity of F with separated endpoints, (ii) a characterization of the nonnegativity of F for the case of general (jointly varying) endpoints, and (iii) several perturbation-type inequalities regarding the nonnegativity of F with zero endpoints. Some of these results are new even for the special case of discrete Hamiltonian systems.
Related projects:	Optimality conditions on time scales Difference Equations and Dynamic Equations on Time Scales. Linear Hamiltonian dynamic systems and half-linear dynamic equations