Multiplicity of solutions for a class of fourth-order elliptic problems with asymptotically linear term

摘要

We study the following fourth-order elliptic equations: Δ ~2u + aΔu = f (x, u), x ∈ Ω, u = Δu = 0, x ∈ ?Ω, where Ω ? ? ~N is a bounded domain with smooth boundary ?Ω and f (x, u) is asymptotically linear with respect to u at infinity. Using an equivalent version of Cerami's condition and the symmetric mountain pass lemma, we obtain the existence of multiple solutions for the equations.