Perturbation of time scale quadratic functionals with variable endpoints

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Authors	HILSCHER Roman RŮŽIČKOVÁ Viera
Year of publication	2007
Type	Article in Periodical
Magazine / Source	Advances in Dynamical Systems and Applications
MU Faculty or unit	Faculty of Science
Citation
Field	General mathematics
Keywords	Linear Hamiltonian system; nonnegativity; positivity; quadratic funcfunctional; time scale; time scale symplectic system
Description	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.
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