Multiplicity results for double eigenvalue problems involving the p-Laplacian

The existence of multiple nontrivial solutions for two types of double eigenvalue problems involving the p-Laplacian is derived. To prove the existence of at least two nontrivial solutions we use a Ricceri-type three critical point result for non-smooth functions of S. Marano and D. Motreanu \cite{MarMot}. The existence of at least three nontrivial solutions is shown by combining a result of B. Ricceri \cite{Ricceri} and a Pucci-Serrin mountain pass type theorem of S. Marano and D. Motreanu \cite{MarMot}.