Abstract:

This article considers the equation
△² u =f(x,u)
with boundary conditions either $u|_{\partial\Omega}=\frac{\partial u}{\partial n}|_{\partial\Omega}=0 $ or $u|_{\partial\Omega}=\bigtriangleup
u|_{\partial\Omega}=0$, where $f(x,t)$ is asymptotically linear with respect to t at infinity, and $\Omega$ 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).

Key words: Biharmonic, mountain pass theorem, asymptotically linear