Detail publikace

Perturbation of nonnegative time scale quadratic functionals

HILSCHER, R. RŮŽIČKOVÁ, V.

Originální název

Perturbation of nonnegative time scale quadratic functionals

Typ

článek ve sborníku ve WoS nebo Scopus

Jazyk

angličtina

Originální abstrakt

In this paper we consider a bounded time scale T=[a,b] , a quadratic functional F(x,u) defined over such time scale, and its perturbation G(x,u)=F(x,u)+\alpha\,|x(a)|2 , where the endpoints of F are zero, while the initial endpoint x(a) of G can vary and x(b) is zero. It is known that there is no restriction on x(a) in G when studying the positivity of these functionals. We prove that, when studying the nonnegativity, the initial state x(a) in G must be restricted to a certain subspace, which is the kernel of a specific conjoined basis of the associated time scale symplectic system. This result generalizes a known discrete-time special case, but it is new for the corresponding continuous-time case. We provide several examples which illustrate the theory.

Klíčová slova

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

Autoři

HILSCHER, R.; RŮŽIČKOVÁ, V.

Vydáno

1. 5. 2007

ISBN

978-981-270-643-0

Kniha

DIFFERENCE EQUATIONS, SPECIAL FUNCTIONS AND ORTHOGONAL POLYNOMIALS Proceedings of the International Conference

Strany od

266

Strany do

275

Strany počet

10

BibTex

@inproceedings{BUT20211,
  author="Roman Šimon {Hilscher} and Viera {Štoudková Růžičková}",
  title="Perturbation of nonnegative time scale quadratic functionals",
  booktitle="DIFFERENCE EQUATIONS, SPECIAL FUNCTIONS AND ORTHOGONAL POLYNOMIALS Proceedings of the International Conference",
  year="2007",
  pages="266--275",
  isbn="978-981-270-643-0"
}