Nehari manifold approach for a singular multi-phase variable exponent problem

TL;DR

This paper investigates a complex multi-phase problem with variable singularities using the Nehari manifold method, establishing the existence of multiple positive solutions with different energy levels.

Contribution

It introduces a novel application of the Nehari manifold approach to a singular multi-phase variable exponent problem, proving the existence of multiple solutions.

Findings

Existence of at least two positive solutions.

Solutions have positive and negative energy levels.

The approach handles variable singularities effectively.

Abstract

This paper is concerned with a singular multi-phase problem with variable singularities. The main tool used is the Nehari manifold approach. Existence of at least two positive solutions with positive-negative energy levels are obtained.