Detail publikace

Perturbation of nonnegative time scale quadratic functionals

HILSCHER, R. RŮŽIČKOVÁ, V.

Anglický název

Perturbation of nonnegative time scale quadratic functionals

Typ

Stať ve sborníku v databázi WoS či Scopus

Jazyk

en

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 anglicky

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

Vydáno

2007-05-01

ISBN

978-981-270-643-0

Kniha

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

Strany od–do

266–275

Počet stran

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"
}