Electronic Journal of Differential Equations,
Vol. 2004(2004), No. 61, pp. 1-15.
Title: Asymptotically almost periodic and almost periodic solutions
for a class of evolution equations
Authors: Eduardo Hernandez M. (Univ. de Sao Paulo, Brazil)
Mauricio L. Pelicer (Univ. de Sao Paulo, Brazil)
Jose P. C. dos Santos (Univ. de Sao Paulo, Brazil)
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.