Positive solutions for a nonhonogeneous semilinear elliptic problem with supercritical exponent (Q5930129)

The authors consider the problem of existence and uniqueness of a positive generalized solution to the boundary value problem NEWLINE\[NEWLINE -\Delta u=\lambda+u^p, \quad u>0, \quad x \in \Omega, NEWLINE\]NEWLINE NEWLINE\[NEWLINEu=0, \quad x \in \partial \Omega,NEWLINE\]NEWLINE where \(\Omega\) is a bounded domain in \(\mathbb{R}^n\) and \(\lambda>0\), \(p>1\). They establish conditions of existence and non-existence of a solution. The most interesting result is that a positive solution of the problem is unique for sufficiently small positive \(\lambda\) when \(p>(N+2)/N-2)\).