On the averaging principle for semilinear functional differential equations with infinite delay in a Banach space (Q2088667)

In this paper, the authors establish several results on the averaging method for some semilinear functional differential equations in Banach spaces. The linear part is assumed to generate a co-semigroup that is not necessarily compact. The non linear part is assumed to be continuous and to satisfy some growth estimation less than the classical Lipschitz condition. The delay is assumed to be infinite and the phase space is axiomatically defined. The authors use the measure of noncompactness and condensing maps to establish the existence and uniqueness of the mild solution.