Fixed point methods and accretivity for perturbed nonlinear equations in Banach spaces

In this paper we use fixed point theorems to guarantee the existence of solutions for inclusions of the form Au + lambda u + Fu (sic) g, where Ais a quasi-m-accretive operator defined in a Banach space, lambda > 0, and the nonlinear perturbation Fsatisfies some suitable conditions. We apply the obtained results, among other things, to guarantee the existence of solutions of boundary value problems of the type -Delta rho(u(x)) + lambda u(x) + Fu(x) = g(x), x epsilon Omega, and rho(u) = 0 on partial derivative Omega, where the Laplace operator.should be understood in the sense of distributions over Omega and to study the existence and uniqueness of solution for a nonlinear integro-differential equation posed in L-1(Omega). (C) 2020 Elsevier Inc. All rights reserved.