Multiplicity of solutions for a class of fourth-order elliptic problems with asymptotically linear term (Q443065)

Summary: We study the following fourth-order elliptic equations: \(\Delta^2 u + a\Delta u = f(x, u), \;x \in \Omega , \;u = \Delta u = 0, \;x \in \partial \Omega\), where \(\Omega \subset \mathbb R^N\) is a bounded domain with smooth boundary \(\partial \Omega\) 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.