文章基本信息

标题：On a higher-order evolution equation with a Stepanov-bounded solution
本地全文：下载
作者：Aribindi Satyanarayan Rao
期刊名称：International Journal of Mathematics and Mathematical Sciences
印刷版ISSN：0161-1712
电子版ISSN：1687-0425
出版年度：2004
卷号：2004
DOI：10.1155/S0161171204306277
出版社：Hindawi Publishing Corporation
摘要：We study strong solutions u:ℝ→X, a Banach space X, of the nth-order evolution equation u(n)−Au(n−1)=f, an infinitesimal generator of a strongly continuous group A:D(A)⊆X→X, and a given forcing term f:ℝ→X. It is shown that if X is reflexive, u and u(n−1) are Stepanov-bounded, and f is Stepanov almost periodic, then u and all derivatives u′,…,u(n−1) are strongly almost periodic. In the case of a general Banach space X, a corresponding result is obtained, proving weak almost periodicity of u, u′,…,u(n−1).