Abstract: Using variational method and a three critical points theorem of Ricceri, we considered a class of quasilinear eigenvalue problemof the formand sufficient conditions which guarantee the existence of at least three weak solutions for the above problem were established. Moreover, the results in the literature are generalized.

Key words: p-Laplacian, Ricceri three critical points theorem, variational method, weak solution, eigenvalue Dirichlet problem