Biharmonic equations with asymptotically linear nonlinearities

This article considers the equationΔ2u = f(x,u)with boundary conditions either u|∂Ω= ∂u∂n|∂Ω=0 or u|∂Ω= Δu|∂Ω=0, where f(x,t) is asymptotically linear with respect to t at infinity, and Ω is a smooth bounded domain in RN, N >4. By a variant version of Mountain Pass Theorem, it is proved that the above problems have a nontrivial solution under suitable assumptions of f(x,t).