Existence and multiplicity of solutions for nonlocal fourth-order elliptic equations with combined nonlinearities

Abstract

This paper is concerned with the following nonlocal fourth-order elliptic problem: 2 u-m(Ω |∇u| 2 dx) u = a(x)|u| s-2 u + f (x, u), x ∈ Ω, u = u = 0, x ∈ ∂Ω, by using the mountain pass theorem, the least action principle, and the Ekeland variational principle, the existence and multiplicity results are obtained.