Existence of Periodic Solutions for Integrodifferential Impulsive Periodic System on Banach Space | Zendy

JinRong Wang | Zendy; Xianbo Xiang | Zendy; Wei Wang | Zendy

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Existence of Periodic Solutions for Integrodifferential Impulsive Periodic System on Banach Space

Author(s) -

JinRong Wang,

Xianbo Xiang,

Wei Wang

Publication year - 2008

Publication title -

abstract and applied analysis

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.228

H-Index - 56

eISSN - 1687-0409

pISSN - 1085-3375

DOI - 10.1155/2008/939062

Subject(s) - banach space , bounded function , mathematics , operator (biology) , impulse (physics) , norm (philosophy) , compact space , bounded operator , mathematical analysis , algorithm , pure mathematics , physics , chemistry , law , biochemistry , repressor , quantum mechanics , political science , transcription factor , gene

This paper deals with a class of integrodifferential impulsive periodic systems on Banach space. Using impulsive periodic evolution operator given by us, the T0-periodic PC-mild solution is introduced and suitable Poincaré operator is constructed. By virtue of the generalized new Gronwall lemma with impulse and B-norm, the estimate on the PC-mild solutions is derived. Showing the continuity and compactness of the Poincaré operator, we utilize Horn's fixed point theorem to prove the existence of T0-periodic PC-mild solutions when the PC-mild solutions are bounded and ultimate bounded. This extends the study of periodic solutions of integrodifferential periodic system without impulse to integrodifferential periodic system with impulse on general Banach spaces. At last, an example is given for demonstration

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