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\Phi -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 C1,τ{C}^{1,\tau } regularity of solutions is also investigated, chiefly via a priori estimates and perturbation techniques.

Keywords

• φ-laplacian
• sobolev-orlicz spaces
• singular terms
• variational methods
• 35j20
• 35j25
• 35j62