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

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  • Qiong Liu
  • Dengfeng Lü

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.

Suggested Citation

  • Qiong Liu & Dengfeng Lü, 2012. "Multiplicity of Solutions for a Class of Fourth-Order Elliptic Problems with Asymptotically Linear Term," Journal of Applied Mathematics, Hindawi, vol. 2012, pages 1-14, June.
    • Handle: RePEc:hin:jnljam:749059
    DOI: 10.1155/2012/749059
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