Zhijun Zhang
Abstract:
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 email: zhangzj@ytu.edu.cn |
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