Infinitely many small energy solutions for Fourth-Order Elliptic Equations with p-Laplacian in [formula omitted

Abstract

In this paper, we study the following fourth-order elliptic equation with p-Laplacian, steep potential well and sublinear perturbation: Δ2u−Δpu+μV(x)u=f(x,u)+ξ(x)|u|q−2u,x∈RN,where N≥5, Δ2≔Δ(Δ) is the biharmonic operator, Δpu=div|∇u|p−2∇u with p>2, μ>0 is a parameter, f∈CRN×R,R, ξ∈L22−qRN with 1≤q<2, we have the potential V∈C(RN,R), and V−1(0) has nonempty interior. Under certain assumptions on V and f, we show the existence nontrivial solutions by virtue of variational methods, the existence criteria of infinitely many nontrivial small energy solutions are established.