Superlinear Elliptic Problems With Sign Changing Coefficients

Abstract

2 Elliptic problems with sign changing coefficients AbstractVia variational methods, we study multiplicity of solutions for the problemwhere a simple example for g(x, u) is |u| p−2 u; here a, λ are real parameters, 1 < q < 2 < p ≤ 2 * and b(x) is a function in a suitable space L σ . We obtain a class of sign changing coefficients b(x) for which two non-negative solutions exist for any λ > 0, and a total of five nontrivial solutions are obtained when λ is small and a ≥ λ 1 . Note that this type of results are valid even in the critical case.