Electron. J. Diff. Equ., Vol. 2010(2010), No. 101, pp. 1-13.

Dependence results on almost periodic and almost automorphic solutions of evolution equations

Joel Blot, Philippe Cieutat, Gaston M. N'Guerekata

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.

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Joël Blot
Laboratoire SAMM EA 4543, Université Paris 1 Panthéon-Sorbonne
centre P.M.F., 90 rue de Tolbiac, 75634 Paris cedex 13, France
email: blot@univ-paris1.fr
Philippe Cieutat
Laboratoire de Mathématiques de Versailles, UMR-CNRS 8100
Université Versailles-Saint-Quentin-en-Yvelines
45 avenue des États-Unis, 78035 Versailles cedex, France
email: Philippe.Cieutat@math.uvsq.fr
Gaston M. N'Guérékata
Department of Mathematics
Morgan State University
1700 E. Cold Spring Lane, Baltimore, MD 21251, USA
email: gnguerek@jewel.morgan.edu

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