Existence of two solutions for singular φ-Laplacian problems

Abstract

Existence of two solutions to a parametric singular quasi-linear elliptic problem is proved. The equation is driven by the Φ-Laplacian operator, and the reaction term can be nonmonotone. The main tools employed are the local minimum theorem and the Mountain pass theorem, together with the truncation technique. Global C^(1,τ) regularity of solutions is also investigated, chiefly via a priori estimates and perturbation techniques.