Multiplicity Of Nontrivial Solutions For Biharmonic Equations With P-Laplacian In R~N

In this paper,we mainly study a class of biharmonic equations with p-LaplacianwhereN?1???R,?>0 is a parameter,?_pu=div(|?u|^p-2?u)withp?2,V?C?R^N?.We obtain the existence of two solutions of the problem as??+?by establishing the mutual restriction between ?,p and f.The proof is mainly obtained by using the Mountain Pass theorem and Ekeland variational principle on the basis of Gagliardo-Nirenberg inequality.