Biharmonic Equations With Asymptotically Linear Nonlinearities

In this paper we study the existence of the following equation△~2u=f(x,u)with boundary conditions either u|(?)Ω=(?)u/(?)n|(?)Ω=0 or u|(?)Ω=△u|(?)Ω=0,whereΩis a smooth bounded domain in R~N, N＞4. In the first chapter, weconsidered that f(x, t) is asymptotically linear with respect to t at infinity,by a variant version of Mountain Pass Theorem, we prove that the aboveproblems have a nontrivial solution under suitable assumptions on f(x, t);In the second chapter, we considered that f(x, t) is superlinear with respectto t at infinity, using Nehari Manifold mathod, we prove that the aboveproblems have a nontrivial solution under suitable assumptions on f(x, t).