Shufang Liu, Yonglin Xu
In this article we study the blow-up rate of solutions near the boundary for the semilinear elliptic problem
where is a smooth bounded domain in , and b(x) is a nonnegative weight function which may be bounded or singular on the boundary, and f is a regularly varying function at infinity. The results in this article emphasize the central role played by the nonlinear gradient term and the singular weight b(x). Our main tools are the Karamata regular variation theory and the method of explosive upper and lower solutions.
Submitted October 4, 2013. Published January 7, 2014.
Math Subject Classifications: 35J25, 35B50, 65J65.
Key Words: Boundary blow-up solutions; nonlinear gradient terms; Karamata regular variation.
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| Shufang Liu |
Department of Mathematics
Gansu Normal University for Nationalities
Hezuo, Gansu 747000, China
| Yonglin Xu |
School of Mathematics and Computer Science Institute
Northwest University for Nationalities
Lanzhou, Gansu 730030, China
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