Geodesic
A remark on the existence of large solutions via sub and supersolutions
Electronic Journal of Differential Equations, Tome 2003 (2003).

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: 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 
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     author = {Garc{\'\i}a-Meli\'an, Jorge},
     title = {A remark on the existence of large solutions via sub and supersolutions},
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     volume = {2003},
     year = {2003},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2003__2003__a1/}
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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__a1/