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

Year 2021, Volume: 50 Issue: 1, 188 - 198, 04.02.2021

Nabil Machrafı

https://doi.org/10.15672/hujms.620711

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.

Keywords

Fixed point, semitopological semigroup, ordered Banach space, normal cone, functional-differential equation, lower and upper solutions

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