Hybrid Nehari-Schauder type fixed point results and applications

TL;DR

This paper introduces a new fixed point approach based on the Nehari manifold method, extending classical techniques with Schauder and Schaefer theorems to solve systems of operator equations.

Contribution

It develops a fixed point version of the Nehari manifold method for systems of operator equations, integrating Schauder and Schaefer fixed point theorems.

Findings

Established a new fixed point theorem for operator systems

Applied the method to nonlinear integral equations

Demonstrated the approach's effectiveness with an example

Abstract

This paper develops a fixed point version of the well-known Nehari manifold method from critical point theory. The main result is formulated for systems of operator equations, relying on the fixed point theorems of Schauder and Schaefer. The framework also allows for potential extensions combining our Nehari type approach with other fixed point principles. To demonstrate the applicability of the method, an example involving a system of nonlinear integral equations is provided.