Large and very singular solutions to semilinear elliptic equations

Andrey Shishkov

We consider equation $-\Delta u+f(x,u)=0$ in smooth bounded domain $\Omega \in {\mathbb{R}}^N$, $N⩾2$, with $f(x,r)>0$ in $\Omega \times {\mathbb{R}}_{+}^1$ and $f(x,r)=0$ on $\partial \Omega$. We find th…