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2011 Existence Conditions for Bounded Solutions of Weakly Perturbed Linear ImpulsiveSystems
Alexander Boichuk, Martina Langerová, Jaroslava Škoríková
Abstr. Appl. Anal. 2011(SI1): 1-13 (2011). DOI: 10.1155/2011/792689


The weakly perturbed linear nonhomogeneous impulsive systems in the form ẋ=A(t)x  +  εA1(t)x  +  f(t),  tR,  tT:={τi}Z, Δx|t=τi=γi+εA1ix(τi-),  τiTR,  γiRn, and iZ are considered. Under the assumption that the generating system (for ε=0) does not have solutions bounded on the entire real axis for some nonhomogeneities and using the Vishik-Lyusternik method, we establish conditions for the existence of solutions of these systems bounded on the entire real axis in the form of a Laurent series in powers of small parameter ε with finitely many terms with negative powers of ε, and we suggest an algorithm of construction of these solutions.


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Alexander Boichuk. Martina Langerová. Jaroslava Škoríková. "Existence Conditions for Bounded Solutions of Weakly Perturbed Linear ImpulsiveSystems." Abstr. Appl. Anal. 2011 (SI1) 1 - 13, 2011.


Published: 2011
First available in Project Euclid: 15 March 2012

zbMATH: 1230.34015
MathSciNet: MR2827385
Digital Object Identifier: 10.1155/2011/792689

Rights: Copyright © 2011 Hindawi

Vol.2011 • No. SI1 • 2011
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