Leggett-Williams fixed point theorem type for sums of operators and application in PDEs

Abstract

. In this paper we present an extension of the original version of Leggett-Williams fi xed point theorem for a k -set contraction perturbed by an expansive operator. Our approach is applied to prove the existence of non trivial positive solutions for initial value problems (IVPs for short) covering a class two-dimensional nonlinear wave equations.