We consider the boundary blow-up nonlinear elliptic problems in a bounded domain with boundary condition , where and . Under suitable growth assumptions on near the boundary and on both at zero and at infinity, we show the existence of at least one solution in . Our proof is based on the method of explosive sub-supersolutions, which permits positive weights which are unbounded and/or oscillatory near the boundary. Also, we show the global optimal asymptotic behaviour of the solution in some special cases.
Submitted May 21, 2005. Published January 6, 2006.
Math Subject Classifications: 35J60, 35B25, 35B50, 35R05.
Key Words: Semilinear elliptic equations; explosive subsolutions; explosive superbsolutions; existence; global optimal asymptotic behaviour.
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| Zhijun Zhang |
Department of Mathematics and Informational Science
Yantai University, Yantai, Shandong, 264005, China
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