A Nehari manifold method for nonvariational problems

TL;DR

This paper extends the Nehari manifold method to nonvariational fixed point problems by constructing a radial energy functional, enabling the discovery of multiple localized solutions in conical annular sets.

Contribution

It introduces a novel approach to apply the Nehari manifold method in nonvariational problems using a generalized energy functional.

Findings

Multiple solutions localized in conical annular sets

Extension of Nehari method to nonvariational framework

Illustrative applications demonstrating the method

Abstract

The aim of this paper is to extend the Nehari manifold method from the variational setting to the nonvariational framework of fixed point equations. This is achieved by constructing a radial energy functional that generalizes the standard one from the variational case. Furthermore, the solutions obtained through our method are localized in conical annular sets, which leads to the existence of multiple solutions. The abstract results are illustrated by two representative applications.