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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
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" }