Abstract:

The paper is mainly concerned with global and boundary asymptotic behavior of classical large solutions to semilinear elliptic equation $\Delta u(x)= a(x)f(u)+ b(x)|\nabla u|^q$, $x\in \Omega$, where $\Omega$ is a bounded smooth domain in $\mathbb R^n$ with $n\geq 2$, $q\in (0, 2]$, $f(s)=s^p$ with $p>0$, or $f(s)=\exp s$, $a, b\in C^\alpha(\Omega)$ which are positive and coupling in $\Omega$, but may vanish or blow up on the boundary properly. A complete classification of solutions is given under the appropriate conditions on $a$ and $b$.

Key words: semilinear elliptic equation, nonlinear gradient terms, weights, large solutions, asymptotic behavior