Infinitely many turning points for some supercritical problems (Q1408579)

The paper is concerned with the problem \[ -\Delta u=\lambda f(u),\quad u>0\text{ in } \Omega \quad \text{and}\quad u=0 \text{ on } \partial\Omega. \] Here \(\Omega\) is a symmetric domain in \(\mathbb{R}^n\) and the nonlinearity \(f\) is asymptotically like a supercritical power at infinity. It is proved that the branch of positive solutions undergoes infinitely many bifurcations as it becomes unbounded. The paper is interesting in the sense that it considers domains which are not necessarily balls.