# Existence, nonexistence and multiplicity of positive solutions for singular boundary value problems involving $\varphi$-Laplacian

## TL;DR

This paper investigates conditions under which positive solutions exist, do not exist, or multiple solutions occur for singular boundary value problems involving the $\

## Contribution

It introduces new fixed point index methods to establish existence, nonexistence, and multiplicity results, including a novel case of three positive solutions.

## Key findings

- Established criteria for existence and nonexistence of solutions.
- Proved the possibility of three positive solutions under certain conditions.
- Applied fixed point index theory to singular $\

## Abstract

In this paper, we establish the results on the existence, nonexistence and multiplicity of positive solutions to singular boundary value problems involving $\varphi$-Laplacian. Our approach is based on the fixed point index theory. The interesting point is that a result for the existence of three positive solutions is given.