Existence of two solutions for singular Φ-Laplacian problems
Pasquale Candito, Umberto Guarnotta, Roberto Livrea
Abstract
Abstract Existence of two solutions to a parametric singular quasi-linear elliptic problem is proved. The equation is driven by the <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"><m:mi mathvariant="normal">Φ</m:mi></m:math> \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 <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"><m:msup><m:mrow><m:mi>C</m:mi></m:mrow><m:mrow><m:mn>1</m:mn><m:mo>,</m:mo><m:mi>τ</m:mi></m:mrow></m:msup></m:math> {C}^{1,\tau } regularity of solutions is also investigated, chiefly via a priori estimates and perturbation techniques.