Abstract
In this paper we study the existence of positive solutions of Berger’s equation with the Navier boundary condition \(\begin{cases} \Delta^2 u-\biggl(a+b\displaystyle\int_\Omega |\nabla u|^2\biggr)\Delta u=\lambda f(u), & x\in \Omega, \\ u=\Delta u=0, &x\in \partial\Omega, \end{cases}\) where \(\lambda\) is a positive parameter, \(f\in C(\mathbb{R},\mathbb{R})\) is a given function, \(a\) and \(b\) are two constants with \(b\geq 0\) , and \(a+bt\) is allowed to be negative for some \(t\geq0\) . The proof of the main results is based on the topological degree theory.
