Nonlinear integral inclusions of Hammerstein type (Q1899886)

The paper is concerned with the integral inclusion of Hammerstein type \(x\in KN_f x\), where \[ Ky (s)= \int_\Omega k(s,t) y(t)dt \] is a (single valued) linear integral operator, and \[ N_f x(t)= \{y(t): y(s)\in f(s, x(s)) \text{ a.e.}\} \] is the (multivalued) nonlinear superposition operator generated by a Carathéodory multifunction \(f\). An existence result is proved based on the Leray-Schauder continuation principle and the Hess-Krasnosel'skij monotonicity principle. Applications are concerned with multivalued elliptic systems, forced periodic oscillations in control systems, and critical points of non-smooth energy functionals.