Shuibo Huang, Wan-Tong Li, Qiaoyu Tian
Abstract:
In this article, we analyze uniqueness and asymptotic behavior
of boundary blow-up non-negative solutions to the semilinear elliptic equation
where
is a bounded smooth domain,
b(x) is a non-negative function on
and f is non-negative on
satisfying some structural conditions. The main novelty
of this paper is that uniqueness is established only by imposing
a control on their growth on the weights b(x) near
and the nonlinear term f at infinite, rather than requiring them to
have a precise asymptotic behavior. Our proof is based on the
method of sub and super-solutions and the Safonov iteration technique.
Submitted July 20, 2012. Published August 21, 2012.
Math Subject Classifications: 35J65, 35J60, 74G30, 35B40.
Key Words: Boundary blow-up solutions; uniqueness; asymptotic behavior.
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Shuibo Huang School of Mathematics and Statistics Lanzhou University Lanzhou, Gansu 730000, China email: huangshuibo2008@163.com | |
Wan-Tong Li School of Mathematics and Statistics Lanzhou University Lanzhou, Gansu 730000, China email: wtli@lzu.edu.cn | |
Qiaoyu Tian Department of Mathematics Gansu Normal University for Nationalities Hezuo, Gansu 747000, China email: tianqiaoyu2004@163.com |
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