A study on a class of weighted elliptic problems with indefinite nonlinearities

Abstract

In this work, we will study the existence of solutions for a class of problems involving the p-Laplacian operator with weight and a nonlinearity that changes sign in a domain Ω ⊂ R N with ∂ Ω smooth and N ≥ 3 . For this class of problems with subcritical growth, we can show the existence of two solutions, one nodal and one that does not change sign in Ω. To class with critical case, we prove the existence of nontrivial solution which does not change sign in Ω.