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

Qiong Liu and Dengfeng Lü

Journal of Applied Mathematics, 2012, vol. 2012, issue 1

Abstract: 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.

Date: 2012
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https://doi.org/10.1155/2012/749059

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Persistent link: https://EconPapers.repec.org/RePEc:wly:jnljam:v:2012:y:2012:i:1:n:749059

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