Abstract
In this article, we investigate the existence of solutions for the indefinite nonlinear fourth order elliptic problem with Navier boundary conditions:
Delta(2)v - Delta v + V-lambda(x)v = f(x, v) in Omega, v = Delta v = 0 on partial derivative Omega,
where Omega is a bounded open domain in R-N, N >= 2, V-lambda(x) is sign-changing weight function. Also, the reaction source term f is not necessary positive. We will prove that for lambda large enough, there exists a nontrivial solution. Our method is a variational one. The most delicate point is to choose the appropriate Sobolev space and the suitable norm.