A fixed point result for semigroups of monotone operators and a solution of discontinuous nonlinear functional-differential equations

Abstract

We improve some fixed point theorems by stating a fixed point result for semigroups of monotone operators in the setting of ordered Banach spaces with a normal cone. We illustrate the usefulness of our results by proving the existence and conditional unicity of a solution of an initial value problem for discontinuous nonlinear functional-differential equations under natural hypotheses involving the order structure of the underlying space.