Geodesic
A remark on the existence of large solutions via sub and supersolutions
Electronic journal of differential equations, Tome 2003 (2003)
We study the boundary blow-up elliptic problem $\Delta u=a(x) f(u)$ in a smooth bounded domain $\Omega\subset \mathbb{R}^N$, with $u|_{\partial\Omega}=+\infty$. Under suitable growth assumptions on $a$ near $\partial\Omega$ and on $f$ both at zero and at infinity, we prove the existence of at least a positive solution. Our proof is based on the method of sub and supersolutions, which permits on the one hand oscillatory behaviour of $f(u)$ at infinity and on the other hand positive weights $a(x)$ which are unbounded and/or oscillatory near the boundary.
Classification : 35J60, 35J25
Keywords: boundary blow-up 
@article{EJDE_2003__2003__a101,
     author = {Garc{\'\i}a-Meli\'an,  Jorge},
     title = {A remark on the existence of large solutions via sub and supersolutions},
     journal = {Electronic journal of differential equations},
     year = {2003},
     volume = {2003},
     zbl = {1040.35026},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2003__2003__a101/}
}
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%A García-Melián,  Jorge
%T A remark on the existence of large solutions via sub and supersolutions
%J Electronic journal of differential equations
%D 2003
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%F EJDE_2003__2003__a101
García-Melián,  Jorge. A remark on the existence of large solutions via sub and supersolutions. Electronic journal of differential equations, Tome 2003 (2003). http://geodesic.mathdoc.fr/item/EJDE_2003__2003__a101/