Publication detail

Perturbation of time scale quadratic functionals with variable endpoints

RŮŽIČKOVÁ, V. HILSCHER, R.

Original Title

Perturbation of time scale quadratic functionals with variable endpoints

Type

journal article - other

Language

English

Original Abstract

In this paper we establish perturbation results pertaining the nonnegativity and positivity of a time scale quadratic functional $\F_0$ and its perturbations of the form $$ \G(x,u)=\F_0(x,u)+\alpha\,\|x(a)\|^2+\beta\,\|x(b)\|^2, $$ where the endpoints of the functional $\F_0$ 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.

Keywords

Quadratic functional, Nonnegativity, Positivity, Time scale, Time scale symplectic system, Linear Hamiltonian system.

Authors

RŮŽIČKOVÁ, V.; HILSCHER, R.

RIV year

2007

Released

31. 12. 2007

Publisher

Research India Publications

ISBN

0973-5321

Periodical

Advances in Dynamical Systems and Applications (ADSA)

Year of study

2

Number

2

State

Republic of India

Pages from

207

Pages to

224

Pages count

18

BibTex

@article{BUT44057,
  author="Viera {Štoudková Růžičková} and Roman Šimon {Hilscher}",
  title="Perturbation of time scale quadratic functionals with variable endpoints",
  journal="Advances in Dynamical Systems and Applications (ADSA)",
  year="2007",
  volume="2",
  number="2",
  pages="207--224",
  issn="0973-5321"
}