| Summary: | We study the bifurcations of the semilinear elliptic forth-order
problem with Navier boundary conditions
$$\displaylines{
\Delta^2 u - \hbox{div} ( c(x) \nabla u ) = \lambda f(u) \quad
\text{in }\Omega, \cr
\Delta u = u = 0 \quad\text{on } \partial \Omega.
}$$
Where $\Omega \subset \mathbb{R}^n$, $n \geq 2$ is a smooth bounded
domain, f is a positive, increasing and convex source term and
$c(x)$ is a smooth positive function on $\overline{\Omega}$ such
that the $L^\infty$-norm of its gradient is small enough. We prove
the existence, uniqueness and stability of positive solutions. We
also show the existence of critical value $\lambda^*$ and the
uniqueness of its extremal solutions.
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