Existence of weighted pseudo anti-periodic solutions to some non-autonomous differential equations

In this paper we first introduce two new concepts called respectively weighted pseudo periodicity and weighted pseudo anti-periodicity, which generalize respectively the well-known notions of periodicity and that of anti-periodicity. Basic properties of these new functions are discussed. Furthermore...

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Bibliographic Details
Published in:Applied mathematics and computation 2012-02, Vol.218 (11), p.6536-6548
Main Authors: Al-Islam, Najja S., Alsulami, Saud M., Diagana, Toka
Format: Article
Language:English
Subjects:
Computation
Dichotomy
Differential equations
Mathematical analysis
Mathematical models
Second-order differential equations
Sectorial operators
Weight
Weighted antiperiodic
Weighted pseudo periodic
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Summary:In this paper we first introduce two new concepts called respectively weighted pseudo periodicity and weighted pseudo anti-periodicity, which generalize respectively the well-known notions of periodicity and that of anti-periodicity. Basic properties of these new functions are discussed. Furthermore, the existence of weighted pseudo anti-periodic solutions to some damped non-autonomous second-order differential equations will be investigated. To illustrate our abstract results, the existence of weighted pseudo anti-periodic solutions to a plate-like equation is discussed.
ISSN:0096-3003
1873-5649
DOI:10.1016/j.amc.2011.12.026