Nonlinear eigenvalue problems for the (p,q)–Laplacian

Abstract

We consider a parametric (p,q)-equations with sign-changing reaction and Robin boundary condition. We show that for all values of the parameter λ bigger than a certain value which we determine precisely, the problem has at least three nontrivial solutions all with sign information and ordered. For the particular case of (p,2)-equations we produce a second nodal solution, for a total of four nontrivial solutions. Under symmetry conditions, we show the existence of infinitely many nodal solutions. The same results are also valid for the Dirichlet problem.