Advances in Dynamical Systems and Applications

  • Year: 2007
  • Volume: 2
  • Issue: 2

Perturbation of time scale quadratic functionals with variable endpoints

  • Author:
  • Roman Hilscher1,, Viera Růžičková2,
  • Total Page Count: 18
  • DOI:
  • Page Number: 207 to 224

1Department of Mathematics and Statistics, Faculty of Science, Masaryk University, Janáčkovo nám. 2a, CZ-60200, Brno, Czech Republic. E-mail: hilscher@math.muni.cz

2Institute of Mathematics, Faculty of Mechanical Engineering, Brno University of Technology, Technická 2, CZ-61669, Brno, Czech Republic. E-mail: ruzickova@fme.vutbr.cz

Abstract

In this paper we establish perturbation results pertaining the nonnegativity and positivity of a time scale quadratic functional and its perturbations of the form where the endpoints of the functional are zero while the endpoints of the functional 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.

Keywords

Linear Hamiltonian system, nonnegativity, positivity, quadratic functional, time scale, time scale symplectic system