Solvability of the Cauchy problem for infinite delay equations Original Research Article

In this paper, we study the solvability of the Cauchy problem for functional differential equations with infinite delay in a Banach space X, which are more general than those in many previous publications. We undertake our study under suitable hypotheses based on noncompactness measures and Kamke-type functions, and in a general setting of admissible phase space View the MathML source including the space Lp((−∞,0],X). Therefore, our results extend and unify many existing results for finite and infinite delay equations. As a sample of possible applications, we analyze the solvability of the Cauchy problem for a Schrödinger-type partial functional integro-differential equation in L1(R).