Pseudo -asymptotically periodic solutions of second-order abstract Cauchy problems

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• 作者：Herná ; n R. Henrí ; quez¹ ; ^a ; ^{hernan.henriquez@usach.cl" class="auth_mail" title="E-mail the corresponding author} ; Michelle Pierri^b ; ^{michellepierri@ffclrp.usp.br" class="auth_mail" title="E-mail the corresponding author} ; Vanessa Rolnik ; ^b ; ^{vanessarolnik@ffclrp.usp.br" class="auth_mail" title="E-mail the corresponding author}
• 关键词：Asymptotically periodic solutions ; Second order abstract Cauchy problem ; Differential equations in abstract spaces ; Mild solutions ; Cosine functions of operators
• 刊名：Applied Mathematics and Computation
• 出版年：2016
• 出版时间：1 February 2016
• 年：2016
• 卷：274
• 期：Complete
• 页码：590-603
• 全文大小：383 K

文摘

In this work we discuss the existence of pseudo S$\mathcal{S}$-asymptotically periodic mild solutions for a second order abstract Cauchy problem. In particular, we show that pseudo S$\mathcal{S}$-asymptotically ω-periodic cosine functions of operators are ω-periodic. The paper is completed with an application to the nonautonomous wave equation.