文章基本信息

标题：Weighted pseudo almost periodic solutions to a class of semilinear integro-differential equations in Banach spaces
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作者：Edgardo Alvarez ; Carlos Lizama
期刊名称：Advances in Difference Equations
印刷版ISSN：1687-1839
电子版ISSN：1687-1847
出版年度：2015
卷号：2015
期号：1
页码：31
DOI：10.1186/s13662-015-0370-5
语种：English
出版社：Hindawi Publishing Corporation
摘要：In this paper we prove the existence of weighted pseudo almost periodic mild solutions for the class of integro-differential equations in the form u ′ ( t ) = A u ( t ) + α ∫ − ∞ t e − β ( t − s ) A u ( s ) d s + f ( t , u ( t ) ) $u'(t)=Au(t)+\alpha\int_{-\infty}^{t}e^{-\beta(t-s)}Au(s) \,ds+f(t,u(t)) $ where f ( ⋅ , u ( ⋅ ) ) $f(\cdot,u(\cdot))$ is a Stepanov-like weighted pseudo almost periodic function and A generates an immediately norm continuous C 0 $C_($ -semigroup on a Banach space X. Also, we give a short proof to show that the vector-valued space of Stepanov-like weighted pseudo almost periodic functions is a Banach space.
关键词：weighted pseudo almost periodic functions ; Stepanov weighted pseudo almost periodic functions ; convolution ; composition ; abstract Volterra equations ; infinite delay