We study the following fourth-order elliptic equations: , where is a bounded domain with smooth boundary and is asymptotically linear with respect to 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.
Qiong Liu. Dengfeng Lü. "Multiplicity of Solutions for a Class of Fourth-Order Elliptic Problems with Asymptotically Linear Term." J. Appl. Math. 2012 1 - 14, 2012. https://doi.org/10.1155/2012/749059