Biharmonic equations with asymptotically linear nonlinearities

This article considers the equation

Δ²u = f(x,u)

with boundary conditions either u|∂Ω=

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 R_N, 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).