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

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• 作者：Najja S. Al-Islam^a ; ^{nal-islam@ccc.edu} ; Saud M. Alsulami^b ; ^{alsulami@kau.edu.sa} ; Toka Diagana^c ; ^{tdiagana@howard.edu} ; ^{tokadiag@gmail.com}
• 关键词：Weight ; Weighted pseudo periodic ; Weighted antiperiodic ; Dichotomy ; Sectorial operators ; Second-order differential equations
• 刊名：Applied Mathematics and Computation
• 出版年：2012
• 出版时间：5 February, 2012
• 年：2012
• 卷：218
• 期：11
• 页码：6536-6548
• 全文大小：264 K

文摘

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.