Electron. J. Diff. Eqns., Vol. 2004(2004), No. 61, pp. 1-15.

Asymptotically almost periodic and almost periodic solutions for a class of evolution equations

Eduardo Hernandez M, Mauricio L. Pelicer, & Jose P. C. dos Santos

Abstract:
In this paper we study the existence of asymptotically almost periodic and almost periodic solutions for the partial evolution equation
$$ \frac{d}{dt} (x(t)+g(t,x(t))=Ax(t)+f(t,Bx(t)), $$
where $A$ is the infinitesimal generator of an analytic semigroup on a Banach space $X$, $B$ is a closed linear operator, and $f$, $g$ are given functions.

Submitted February 20, 2004. Published April 21, 2004.
Math Subject Classifications: 34K14, 34K30.
Key Words: Almost periodic, asymptotically almost periodic, semigroup of linear operators.

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Eduardo Hernandez M.
Departamento de Matematica
Instituto de Ciencias Matematicas de Sao Carlos
Universidade de Sao Paulo, Caixa Postal 668
13560-970 Sao Carlos, SP. Brazil
email: lalohm@icmc.sc.usp.br
Mauricio L. Pelicer
Departamento de Matematica
Instituto de Ciencias Matematicas de Sao Carlos
Universidade de Sao Paulo, Caixa Postal 668
13560-970 Sao Carlos, SP. Brazil
email: mpelicer@icmc.sc.usp.br
Jose P. C. dos Santos
Departamento de Matematica
Instituto de Ciencias Matematicas de Sao Carlos
Universidade de Sao Paulo, Caixa Postal 668
13560-970 Sao Carlos, SP. Brazil
email: zepaulo@icmc.sc.usp.br

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