加权椭圆系统稳定解的单调公式的一个注记

数学物理学报 ›› 2017, Vol. 37 ›› Issue (4): 698-705.

加权椭圆系统稳定解的单调公式的一个注记

鲁萍萍, 胡良根

宁波大学数学系浙江宁波 315211

收稿日期:2016-12-27 修回日期:2017-04-16 出版日期:2017-08-26 发布日期:2017-08-26
作者简介:胡良根,E-mail:hulianggen@tom.com
基金资助:
国家自然科学基金（11201248，11471174）、浙江省自然科学基金（LY17A010007）和宁波市自然科学基金（2016A610073）

A Note to Monotonicity Formula for Stable Solutions of the Weighted Elliptic System

Lu Pingping, Hu Lianggen

Department of Mathematics, Ningbo University, Zhejiang Ningbo 315211

Received:2016-12-27 Revised:2017-04-16 Online:2017-08-26 Published:2017-08-26
Supported by:
Supported by the NSFC (11201248, 11471174), the Natural Science Foundation of Zhejiang Province (LY17A010007) and the Natural Science Foundation of Ningbo (2016A610073)

摘要/Abstract

摘要： 利用分析的技巧重新构造了加权椭圆系统稳定解的单调公式.相比于文献[12，定理2.1]，该文的构造方法计算简便直接.

关键词: 加权椭圆系统, 稳定解, 单调公式

Abstract: In this paper, we reconstruct a monotonicity formula for stable solution of the weighted elliptic system by the use of analysis technique. In contrast with[12, Theorem 2.1], the construction of method is more convenient and direct to compute.

Key words: The weighted elliptic system, Stable solution, Monotonicity formula

中图分类号:

O175.25

鲁萍萍, 胡良根. 加权椭圆系统稳定解的单调公式的一个注记[J]. 数学物理学报, 2017, 37(4): 698-705.

Lu Pingping, Hu Lianggen. A Note to Monotonicity Formula for Stable Solutions of the Weighted Elliptic System[J]. Acta mathematica scientia,Series A, 2017, 37(4): 698-705.

参考文献

[1] de Figueiredo D G, Felmer P L. A Liouville type theorem for elliptic systems. Ann Scuola Norm Sup Pisa, 1994, 21:387-397
[2] Mitidieri E. A Rellich type identity and applications. Comm Partial Differential Equations, 1993, 18:125-151
[3] Souplet Ph. The proof of the Lane-Emden conjecture in four space dimensions. Adv Math, 2009, 221:1409-1427
[4] 肖迎迎, 郑雄军. Morse指数与带权的椭圆方程的Liouville型定理. 数学物理学报, 2016, 36A(3):493-499 Xiao Y Y, Zheng X J. Morse indices and Liouville type theorems for weighted elliptic equations. Acta Math Sci, 2016, 36A(3):493-499
[5] 胡良根. 非线性Hénon方程解的Liouville定理. 数学物理学报, 2016, 36A(4):639-648 Hu L G. Liouville type theorems of solutions for the nonlinear Hénon equations. Acta Math Sci, 2016, 36A(4):639-648
[6] Pacard F. Partial regularity for weak solutions of a nonlinear elliptic equations. Manuscipta Math, 1993, 79:161-172
[7] Pacard F. Convergence and partial regularity for weak solutions of some nonlinear elliptic equation:the supercritical case. Ann I H Poincaré Anal Non-Linéaire, 1994, 11:537-551
[8] Dávila J, Dupaigne L, Wang K L, Wei J C. A monotonicity formula and a Liouville-type Theorem for a forth order supercritical problem. Adv Math, 2014, 258:240-285
[9] Hu L G. Liouville-type theorems for the fourth order nonlinear elliptic equation. J Differential Equations, 2014, 256:1817-1846
[10] Du Y H, Guo Z M, Wang K L. Monotonicity formula and ε-regularity of stable solutions to supercritical problems and applications to finite Morse index solutions. Calc Var Partial Differential Equations, 2014, 50:615-638
[11] Fazly M, Wei J C. On stable solutions of the fractional Hénono-Lane-Emden equation. Commun Contemp Math, 2016, 18:1650005
[12] Hu L G. A monotonicity formula and Liouville-type theorems for stable solutions of the weighted elliptic system. Adv Differential Equations, 2017, 22:49-76
[13] Luo S P, Wei J C, Zou W M. On the triharmonic Lane-Emden equation. 2016, arXiv:1607.04719