EXISTENCE OF LARGE SOLUTIONS FOR A SEMILINEAR ELLIPTIC PROBLEM VIA EXPLOSIVE SUB- SUPERSOLUTIONS
Zhijun Zhang · DOAJ (DOAJ: Directory of Open Access Journals) · 2006
We consider the boundary blow-up nonlinear elliptic problems $Delta upmlambda | abla u|^q=k(x)g(u)$ in a bounded domain with boundary condition $u|_{partial Omega}=+infty$, where $qin [0, 2]$ and $lambdageq0$. Under suitable growth assumptions on $k$ near the boundary and on $g$ both at zero and at infinity, we show the existence of at least one solution in $C^2(Omega)$. Our proof is based on the method of explosive sub-supersolutions, which permits positive weights $k(x)$ which are unbounded and/or oscillatory near the boundary. Also, we show the global optimal asymptotic behaviour of the solution in some special cases.