Solvability of inclusions of Hammerstein type

Abstract

We establish a universal rule for solving operator inclusions of Hammerstein type in Lebesgue-Bochner spaces with the aid of some recently proven continuation theorem of Leray-Schauder type for the class of so-called admissible multimaps. Examples illustrating the legitimacy of this approach include the initial value problem for perturbation of m-accretive mutivalued differential equation, the nonlocal Cauchy problem for semilinear differential inclusion, abstract integral inclusion of Fredholm and Volterra type and the two-point boundary value problem for nonlinear evolution inclusion.2010 Mathematics Subject Classification. 34A60, 34G25, 45N05, 47H10, 47H30. Key words and phrases. acyclic set, admissible map, boundary value problem, evolution inclusion, fixed point, integral inclusion, m-accretive, operator inclusion, p-integrable solution.