Geodesic
Existence of large solutions for a semilinear elliptic problem via explosive sub- supersolutions
Electronic journal of differential equations, Tome 2006 (2006)
We consider the boundary blow-up nonlinear elliptic problems $\Delta u\pm\lambda |\nabla u|^q=k(x)g(u)$ in a bounded domain with boundary condition $u|_{\partial \Omega}=+\infty$, where $q\in [0, 2]$ and $\lambda\geq0$. 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.
Classification : 35J60, 35B25, 35B50, 35R05
Keywords: semilinear elliptic equations, explosive subsolutions, explosive superbsolutions, existence, global optimal asymptotic behaviour 
@article{EJDE_2006__2006__a172,
     author = {Zhang,  Zhijun},
     title = {Existence of large solutions for a semilinear elliptic problem via explosive sub- supersolutions},
     journal = {Electronic journal of differential equations},
     year = {2006},
     volume = {2006},
     zbl = {1284.35189},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2006__2006__a172/}
}
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%A Zhang,  Zhijun
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%J Electronic journal of differential equations
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Zhang,  Zhijun. Existence of large solutions for a semilinear elliptic problem via explosive sub- supersolutions. Electronic journal of differential equations, Tome 2006 (2006). http://geodesic.mathdoc.fr/item/EJDE_2006__2006__a172/