Almost automorphic mild solutions for some semilinear abstract dynamic equations on time scales

  • G. M. N’Gu'er'ekata
  • Gis'ele Mophou
  • Aril Milc'e

Abstract

This paper deals with the semilinear dynamic equation $$x^\Delta(t)=Ax(t)+f(t,x(t)),\hbox{    } t\in\T$$  in a abstract Banach space $\X$, where $A$ is the infinitesimal generator of an exponentially stable $C_0$-semigroup on time scales.  Under suitable conditions on $f$ defined on time scale,  we establish the existence and the uniqueness of  almost automorphic mild solution  to this problem. The result is achieved  by means of the Banach Fixed-Point Theorem. Finally, we establish a correspondence between linear and nonlinear equations.
Published
2015-08-28
Section
Articles