Multiplicity of Solutions for a Class of Fourth-Order Elliptic Problems with Asymptotically Linear Term

Abstract EN

We study the following fourth-order elliptic equations: Δ2u+aΔu=f(x,u), x∈Ω, u=Δu=0, x∈∂Ω, where Ω⊂ℝN 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.