Existence of two solutions for singular {\Phi}-Laplacian problems

TL;DR

This paper proves the existence of two solutions for a class of singular {\

Contribution

It introduces new methods to establish multiple solutions for {\

Findings

Existence of two solutions is established.

Solutions possess global C^{1,{\

paper_type":"theoretical"}}}}

Abstract

Existence of two solutions to a parametric singular quasi-linear elliptic problem is proved. The equation is driven by the {\Phi}-Laplacian operator and the reaction term can be non-monotone. The main tools employed are a local minimum theorem and the Mountain Pass theorem, together with the truncation technique. Global C^{1,{\tau}} regularity of solutions is also investigated, chiefly via a priori estimates and perturbation techniques.