On a version of hybrid existence result for a system of nonlinear equations

TL;DR

This paper develops hybrid existence results for a system of nonlinear equations by integrating monotonicity theory and fixed point methods, with applications to boundary value problems involving mixed conditions.

Contribution

It introduces a novel approach combining monotonicity and fixed point theories to establish existence results for nonlinear systems.

Findings

Established hybrid existence theorems for nonlinear operator systems.

Applied results to boundary value problems with mixed nonlocal and Dirichlet conditions.

Extended classical theorems to more complex boundary value scenarios.

Abstract

Combining monotonicity theory related to the parametric version of the Browder-Minty Theorem with fixed point arguments we obtain hybrid existence results for a system of two operator equations. Applications are given to a system of boundary value problems with mixed nonlocal and Dirichlet conditions.