LIOUVILLE TYPE RESULTS AND REGULARITY OF THE EXTREMAL SOLUTIONS OF BIHARMONIC EQUATION WITH NEGATIVE EXPONENTS

被引：23
|
作者：
Guo, Zongming [1 ]
Wei, Juncheng [2 ,3 ]
机构：
[1] Henan Normal Univ, Dept Math, Xinxiang 453007, Peoples R China
[2] Univ Hong Kong, Dept Math Chinese, Shatin, Hong Kong, Peoples R China
[3] Univ British Columbia, Dept Math, Vancouver, BC V6T 1Z2, Canada
来源：
DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS | 2014年 / 34卷 / 06期
基金：
加拿大自然科学与工程研究理事会;
关键词：
Stable entire solutions; biharmonic equations with singularity; regularity of the extremal solutions; POSITIVE SOLUTIONS; ELLIPTIC EQUATION; STABLE-SOLUTIONS; COMPACTNESS; STABILITY;
D O I：
10.3934/dcds.2014.34.2561
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
We first obtain Liouville type results for stable entire solutions of the biharmonic equation -Delta(2)u = u(-p) in R-N for p > 1 and 3 <= N <= 12. Then we consider the Navier boundary value problem for the corresponding equation and improve the known results on the regularity of the extremal solution for 3 <= N <= 12. As a consequence, in the case of p = 2, we show that the extremal solution u* is regular when N = 7. This improves earlier results of Guo-Wei [20] (N <= 4), Cowan-Esposito-Ghoussoub [2] (N = 5), Cowan-Ghoussoub [4] (N = 6).
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页码：2561 / 2580
页数：20
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