# Positive solutions for nonlinear parametric singular Dirichlet problems

## TL;DR

This paper studies positive solutions for a nonlinear Dirichlet problem involving the p-Laplace operator with a parametric singular term and a Carathéodory perturbation, providing a bifurcation analysis of solutions depending on the parameter.

## Contribution

It introduces a bifurcation theorem characterizing how positive solutions vary with the parameter in a singular p-Laplace problem.

## Key findings

- Established existence of positive solutions for the problem.
- Described the exact dependence of solutions on the parameter.
- Provided a bifurcation-type theorem for the solution set.

## Abstract

We consider a nonlinear parametric Dirichlet problem driven by the $p$-Laplace differential operator and a reaction which has the competing effects of a parametric singular term and of a Carath\'eodory perturbation which is ($p-1$)-linear near $+\infty$. The problem is uniformly nonresonant with respect to the principal eigenvalue of $(-\Delta_p,W^{1,p}_0(\Omega))$. We look for positive solutions and prove a bifurcation-type theorem describing in an exact way the dependence of the set of positive solutions on the parameter $\lambda>0$.