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

Authors : Nabil MACHRAFI

Pages : 188-198

Doi:10.15672/hujms.620711

View : 25 | Download : 8

Publication Date : 2021-02-04

Article Type : Research Paper

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