Existence of weighted pseudo almost periodic mild solutions for nonlocal semilinear evolution equations

Abstract

In this paper, we are concerned with new weighted pseudo almost periodic solutions of the semilinear evolution equations with nonlocal conditions

x'(t)=A(t)x(t) + f(t,x(t)), x(0) = x₀ + g(x), t ∈ ℝ⁺.

By applying the Banach fixed point theorem, the theory of the measure theory, the theory of semigroups of operators to evolution families and the properties of a class of new weighted pseudo almost periodic functions which proposed by Blot et al. Recently, some reasonable conditions for the existence and uniqueness of new weighted pseudo almost periodic mild solutions are established.