On the extremal solutions of semilinear elliptic problems. (English) Zbl 1236.35054

Ben Chaabane, Lamia

Abstr. Appl. Anal. 2005, No. 1, 1-9 (2005).

Summary: We investigate here the properties of extremal solutions for semilinear elliptic equation \(-\Delta u=\lambda f(u)\) in \(\Omega\), \(u>0\) in \(\Omega\), \(u=0\) on \(\partial\Omega\), where \(\lambda>0\), posed on a bounded smooth domain \(\Omega\) of \(\mathbb R^n\) with Dirichlet boundary condition and with \(f\) exploding at a finite positive value \(a\).

MSC:

35J61

Semilinear elliptic equations