Locally Lipschitz composition operators and applica- tions to nonlinear integral equations

Abstract

It is well known that imposing a global Lipschitz condition on nonlinear composition operators leads to a strong degeneracy phenomenon in many function spaces. In contrast to this, we show that a local version of Banach's contraction mapping principle is less restrictive and applies to a large variety of nonlinear problems. We illustrate this by means of applications to nonlinear integral equations with bounded or weakly singular kernels.