Uniqueness and asymptotic behaviour for solutions of semilinear problems with boundary blow-up
Uniqueness and asymptotic behaviour for solutions of semilinear problems with boundary blow-up
In this paper we prove uniqueness of positive solutions to logistic singular problems $-\Delta u=\lambda (x) u -a(x) u^{p}$, $u_{|\partial \Omega }=+\infty$, $p>1$, $a>0$ in $\Omega$, where the main feature is the fact that $a_{|\partial \Omega }=0$. More importantly, we provide exact asymptotic estimates describing, in the form of a …