# Positive solutions for weighted singular $p$-Laplace equations via Nehari manifolds

## TL;DR

This paper establishes the existence of multiple positive solutions for weighted singular p-Laplace equations with discontinuous weights using Nehari manifold techniques, addressing challenges posed by irregular weights.

## Contribution

The paper introduces a novel approach employing Nehari manifolds to prove multiple positive solutions for weighted singular p-Laplace equations with discontinuous weights.

## Key findings

- Existence of at least two positive bounded solutions
- Application of Nehari manifold method to irregular weights
- Handling of discontinuous weight functions in singular equations

## Abstract

In this paper we study weighted singular $p$-Laplace equations involving a bounded weight function which can be discontinuous. Due to its discontinuity classical regularity results cannot be applied. Based on Nehari manifolds we prove the existence of at least two positive bounded solutions of such problems.