We investigate a class of nonlinear biharmonic equations with
p-Laplacian
where
805721277d205f9cf" title="Click to view the MathML source">N≥1,
β∈R,
λ>0 is a parameter and
Δpu=div(|∇u|p−2∇u) with
p≥2. Unlike most other papers on this problem, we replace Laplacian with
p-Laplacian and allow
β to be negative. Under some suitable assumptions on
V(x) and
f(x,u), we obtain the existence and multiplicity of nontrivial solutions for
λ large enough. The proof is based on variational methods as well as Gagliardo–Nirenberg inequality.