Asymptotic behaviour of solutions of semilinear equations with subcritical nonlinearity (Q1327675)

Let \(\Omega\) be a bounded smooth domain in \(\mathbb{R}^ n\) \((n \geq 2)\) and consider the problem \(P(\beta) \qquad - \Delta u = \beta f(u)\quad \text{ in } \Omega, \quad u = 0\quad \text{ on } \partial \Omega\) where \(f\) is a positive \(C^ 1\)-function and \(\beta>0\). It is known that under certain further conditions on \(f\) there exists \(I = (0, \tilde \beta)\) such that the problem \(P(\beta)\) has two solutions for any \(\beta \in I\). In this note the author studies asymptotic behaviour and interior oscillations of large solutions of \(P(\beta)\).