Find in Library

We prove the existence of a nonzero solution for the fourth order elliptic equation $$Delta^2u= mu u +a(x)g(u)$$ with boundary conditions $u=Delta u=0$. Here, $mu$ is a real parameter, $g$ is superlinear both at zero and infinity and $a(x)$ changes sign in $Omega$. The proof uses a variational argument based on the argument by Bahri-Lions cite{BL}.