Weighted pseudo almost periodic solutions to a class of semilinear integro-differential equations in Banach spaces

被引：11

作者：

Alvarez, Edgardo ^{[1
]}

Lizama, Carlos ^{[2
]}

机构：

[1] Univ Atlantico, Fac Ciencias Basicas, Dept Matemat, Barranquilla, Colombia

[2] Univ Santiago Chile, Fac Ciencia, Dept Matemat & Ciencia Computac, Santiago, Chile

来源：

ADVANCES IN DIFFERENCE EQUATIONS | 2015年

关键词：

weighted pseudo almost periodic functions; Stepanov weighted pseudo almost periodic functions; convolution; composition; abstract Volterra equations; infinite delay; FUNCTIONAL-DIFFERENTIAL EQUATIONS; EVOLUTION-EQUATIONS; AUTOMORPHIC-FUNCTIONS;

D O I：

10.1186/s13662-015-0370-5

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

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) = Au(t) + alpha integral(t)(-infinity) e(-beta(t-s)) Au(s) ds + f(t, u(t)) where f (., u(.)) is a Stepanov-like weighted pseudo almost periodic function and A generates an immediately norm continuous C-0-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.

引用

页数：18

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