Department of Mathematical Sciences, University of Memphis, Memphis, Tennessee 38152-3240 ; Department of Mathematics, Morgan State University, Baltimore, Maryland 21251
Abstract:
We are concerned with the semilinear differential equation in a Banach space ,
where generates an exponentially stable -semigroup and is a function of the form . Under appropriate conditions on and , and using the Schauder fixed point theorem, we prove the existence of an almost automorphic mild solution to the above equation.