Stepanov-like almost automorphic solutions of nonautonomous semilinear evolution equations with delay Original Research Article

We consider the existence and uniqueness of a Stepanov-like almost automorphic solution to the nonautonomous semilinear evolution equations with a constant delay: View the MathML sourceu′(t)=A(t)u(t)+f(t,u(t−h)),t∈R Turn MathJax on where A(t),t∈RA(t),t∈R, generates an exponentially stable evolution family {U(t,s)}{U(t,s)} and f:R×X→Xf:R×X→X satisfies a Lipschitz condition with respect to the second argument.