Superlinear Elliptic Problems with Sign Changing Coefficients

Via variational methods, we study multiplicity of solutions for the problem {-?u = ?b(x)|u| q-2u + au + g(x, u) in ?, u = 0 on ?, where a simple example for g(x, u) is |u| p-2u; here a, ? are real parameters, 1 < q < 2 < p ? 2* and b(x) is a function in a suitable space L ?. We obtain a class of sign changing coefficients b(x) for which two non-negative solutions exist for any ? > 0, and a total of five nontrivial solutions are obtained when ? is small and a < ? 1. Note that this type of results are valid even in the critical case. © World Scientific Publishing Company.