R.Hilscher, V.Ruzickova

Perturbation of time scale quadratic functionals with variable endpoints

Abstract

In this paper we establish perturbation results pertaining the nonnegativity and positivity of a time scale quadratic functional F0 and its perturbations of the form

G(x,u) = F0(x,u) + \alpha ||x(a)||2 + \beta ||x(b)||2,

where the endpoints of the functional F0 are zero while the endpoints of the functional G can vary. These functionals are closely related to time scale symplectic systems. Moreover, we extend such results to functionals with variable endpoints. The results of this paper generalize perturbation results recently known for the special case of the discrete time, but they are new for the continuous time.


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Last change: October 4, 2007. (c) Roman Hilscher