Electronic Journal of Differential Equations,
Vol. 2010(2010), No. 101, pp. 1-13.
Title: Dependence results on almost periodic and almost automorphic
solutions of evolution equations
Authors: Joel Blot (Univ. Paris 1 Pantheon-Sorbonne, France)
Philippe Cieutat (Univ. Versailles-Saint-Quentin-en-Yvelines, France)
Gaston M. N'Guerekata (Morgan State Univ., Baltimore, MD, USA)
Abstract:
We consider the semilinear evolution equations
$x'(t) = A(t) x(t) + f(x(t), u(t),t)$ and
$x'(t) = A(t) x(t) + f(x(t), \zeta,t)$ where $A(t)$
is a unbounded linear operator on a Banach space X and f
is a nonlinear operator. We study the dependence of solutions
x with respect to the function $u$ in three cases: the continuous
almost periodic functions, the differentiable almost periodic
functions, and the almost automorphic functions. We give results
on the continuous dependence and on the differentiable dependence.
Submitted May 25, 2010. Published July 21, 2010.
Math Subject Classifications: 47J35, 43A60, 47D06.
Key Words: Semilinear evolution equation; almost periodic function;
almost automorphic function; dependence results.