Uniqueness of large positive solutions (Q1684435)

Let \(\Omega\) be a smooth bounded domain in \({\mathbb R}^N\). This paper is concerned with the uniqueness of blow-up boundary solutions for the logistic-type equation \(-\Delta u=\lambda u-a(x)f(u)\) in \(\Omega\), where \(\lambda\) is a real parameter, \(a\) is a non-negative potential, and \(f\) is a non-decreasing function that is super-homogeneous of degree \(p>1\). The main results establish very refined properties, which extend several previous important contributions and open perspectives in the analysis of singular solutions of nonlinear elliptic equations.