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 . The existence of at least three nontrivial solutions is shown by combining a result of B. Ricceri  and a Pucci-Serrin mountain pass type theorem of S. Marano and D. Motreanu .
"MULTIPLICITY RESULTS FOR DOUBLE EIGENVALUE PROBLEMS INVOLVING THE p-LAPLACIAN." Taiwanese J. Math. 13 (3) 1095 - 1110, 2009. https://doi.org/10.11650/twjm/1500405462