Weighted pseudo almost periodic mild solutions of semilinear evolution equations with nonlocal conditions

In this paper, applying the theory of semigroups of operators to evolution families and Banach fixed point theorem, we prove the existence and uniqueness of the weighted pseudo almost periodic mild solution of the semilinear evolution equation x′(t)=A(t)x(t)+f(t,x(t))x′(t)=A(t)x(t)+f(t,x(t)) with nonlocal conditions x(0)=x0+g(x)x(0)=x0+g(x) in Banach space X under some suitable hypotheses.