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Journal of Applied Mathematics
Volume 2012, Article ID 749059, 14 pages
Research Article

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

School of Mathematics and Statistics, Hubei Engineering University, Hubei, Xiaogan 432000, China

Received 10 January 2012; Accepted 5 April 2012

Academic Editor: Turgut Γ–ziş

Copyright © 2012 Qiong Liu and Dengfeng Lü. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


We study the following fourth-order elliptic equations: Ξ” 2 𝑒 + π‘Ž Ξ” 𝑒 = 𝑓 ( π‘₯ , 𝑒 ) , π‘₯ ∈ Ξ© , 𝑒 = Ξ” 𝑒 = 0 , π‘₯ ∈ πœ• Ξ© , where Ξ© βŠ‚ ℝ 𝑁 is a bounded domain with smooth boundary πœ• Ξ© and 𝑓 ( π‘₯ , 𝑒 ) is asymptotically linear with respect to 𝑒 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.