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

Qiong Liu and Dengfeng Lã¼

Journal of Applied Mathematics, 2012, vol. 2012, 1-14

Abstract:

We study the following fourth-order elliptic equations: Δ 2 ð ‘¢ + ð ‘Ž Δ ð ‘¢ = ð ‘“ ( ð ‘¥ , ð ‘¢ ) , ð ‘¥ ∈ Ω , ð ‘¢ = Δ ð ‘¢ = 0 , ð ‘¥ ∈ 𠜕 Ω , where Ω ⊂ â„ ð ‘ is a bounded domain with smooth boundary 𠜕 Ω and ð ‘“ ( ð ‘¥ , ð ‘¢ ) is asymptotically linear with respect to ð ‘¢ 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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Persistent link: https://EconPapers.repec.org/RePEc:hin:jnljam:749059

DOI: 10.1155/2012/749059

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