Existence and multiplicity of nontrivial solutions for some biharmonic equations with p-Laplacian

We investigate a class of nonlinear biharmonic equations with p-Laplacian {Delta(2)u - beta Delta(p)u + lambda V(x)u = f(x,u) in R-N, u is an element of H-2(R-N), where N >= 1, beta is an element of R, lambda > 0 is a parameter and Delta(p)u = div(|del u|(p-2)Vu) with p >= 2. Unlike most other papers on this problem, we replace Laplacian with p-Laplacian and allow beta to be negative. Under some suitable assumptions on V(x) and f(x, u), we obtain the existence and multiplicity of nontrivial solutions for lambda large enough. The proof is based on variational methods as well as Gagliardo-Nirenberg inequality. (C) 2016 Elsevier Inc. All rights reserved.