[1]朱立平,张正策.一类半线性椭圆型方程组正解的存在性与不存在性[J].南京师大学报(自然科学版),2006,29(01):25-29.
　Zhu Liping~,Zhang Zhengce~.Nonexistence and Existence of Positive Solutions of Semilinear Elliptic Systems[J].Journal of Nanjing Normal University(Natural Science Edition),2006,29(01):25-29.
点击复制

一类半线性椭圆型方程组正解的存在性与不存在性()
分享到：

《南京师大学报（自然科学版）》[ISSN:1001-4616/CN:32-1239/N]

卷:
第29卷
期数:
2006年01期
页码:
25-29
栏目:
数学
出版日期:
2006-03-30

文章信息/Info

Title:
Nonexistence and Existence of Positive Solutions of Semilinear Elliptic Systems
作者:
朱立平1;  张正策2
( 1. 西安建筑科技大学理学院, 陕西西安710054)
( 2. 西安交通大学理学院, 陕西西安710049)
Author(s):
Zhu Liping~1; Zhang Zhengce~2
1.College of Science,Xi’an University of Architecture and Technology,Xi’an 710054,China
关键词:
存在性;  不存在性;  移动球面法
Keywords:
ex istence;  nonex istence;  m ethod of m ov ing sphe res
分类号:
O175.25
摘要:
通过Kelvin变换,对移动平面法作了重要的改进和简化,利用移动球面法证明了一类半线性椭圆型方程组古典正解的存在性与不存在性定理;移动球面法并不需要方程组的极大值原理,推广了应用积分法得到的结果,而且还证明了临界情形时古典正解的确切形式;此外,移动球面法也容易推广应用到一般非线性椭圆方程(组)的L iouville问题.
Abstract:
In th is paper, we introduce the Ke lv in transform s and apply the me thod of m ov ing spheres w hich is the sign ificant s imp lifica tions of mov ing plane m ethod to prove the ex istence and nonex istence of positive so lutions for a c lass of sem ilinear e lliptic systems. Them ethod of mov ing spheres doesn t’ not need the m ax im um princ ip le for elliptic sy stem s and ob tains the ex act fo rm of positive so lutions for the critical case wh ich ex tends the resu lts proved by the integ ra lm ethod. M oreover, thism ethod  is also used to prove the Liouv ille theorems for the general non linear e lliptic equations or systems.

参考文献/References:

[ 1] G idas B, Spruck J. G loba l and local behav iour o f positive so lu tions o f non linear elliptic equa tions [ J]. Comm Pure Appl M a th, 1981, 34( 6): 525-598.
[ 2] M itid ieri E. Nonex istence o f positive solutions of sem ilinear e lliptic system s in RN [ J]. D iff Integ ral Eqns, 1996, 9 ( 3): 465-479.
[ 3] De Figue iredo D G, Fe lm er P L. A L iouville-type theo rem fo r elliptic sy stem s [ J]. Ann Scuo la No rm Sup Pisa, 1994, 21 ( 3): 387-397.
[ 4] Busca J, M an-sevich R. A Liouv ille-type theo rem for Lane-Emden system s [ J] . Ind iana UnivM a th J, 2002, 51( 1): 37- 51.
[ 5] Zhang Z C, W angW M, Li K T. L iouville-type theo rem s for sem ilinear e lliptic system s [ J]. J Partial Diff Eqns, 2005, 18( 4): 304-310.
[ 6] L iY Y, ZhuM. Un iqueness theo rem s through them ethod ofm ov ing spheres [ J]. DukeM a th J, 1995, 80( 2): 383-417.
[ 7] Li Y Y, Zhang L. Liouv ille-type theorem s and H arnack-type inequa lities for sem ilinear elliptic equations [ J]. J d- Analyse M a th, 2003, 90: 27-87.
[ 8] Lin C S. A c lassifica tion o f solutions of a con fo rm ally invarian t fou rth order equa tion in RN [ J]. Comm entM athH elv, 1998, 73( 2): 206-231.
[ 9] Peletier L A, V an De rVorst R C A M. Ex istence and non-existence o f positive so lutions of non-linear elliptic system s and the b iharm on ic equation [ J]. D iff Int Eqns, 1992, 5( 4) : 747-767.
[ 10] Se rr in J, Zou H. The ex istence o f positive entire so lutions of ellipticH am itonian system s [ J]. Comm Part Diff Eqns, 1998, 23( 3 /4): 577-599.
[ 11] Zhang Z C, LiK T. Spike-layered so lutions o f singu la rly perturbed quasilinearD irich let problem s [ J]. JM a th AnalAppl, 2003, 283( 2): 667-680.
[ 12] Zhang Z C, Li K T. Spike-layered so lu tions with com pact support to some s ingu lar ly perturbed quasilinear e lliptic problems in general smooth domains [ J]. J Comp ApplM ath, 2004, 162( 2): 327-340.

相似文献/References:

[1]陈莉,袁俊丽.一类p-Laplacian椭圆型方程边值问题的解[J].南京师大学报(自然科学版),2012,35(03):31.
　Chen Li,Yuan Junli.Solutions for a Class of p-Laplacian Elliptic Boundary Value Problem[J].Journal of Nanjing Normal University(Natural Science Edition),2012,35(01):31.
[2]周杰,杨作东.一类拟线性椭圆型方程正奇异解的能量估计[J].南京师大学报(自然科学版),2006,29(01):21.
　Zhou Jie,Yang Zuodong.Energy Estimate of Positive Singular Solutions for a Class Quasilinear Elliptic Equations[J].Journal of Nanjing Normal University(Natural Science Edition),2006,29(01):21.
[3]张康群,孙福树,赵国俊.一类半线性Keldysh型方程解的注记[J].南京师大学报(自然科学版),2013,36(02):5.
　Zhang Kangqun,Sun Fushu,Zhao Guojun.A Note on the Solution of a Class of Keldysh-Type Equations[J].Journal of Nanjing Normal University(Natural Science Edition),2013,36(01):5.
[4]郭金勇.退化拟抛物方程弱解的存在性[J].南京师大学报(自然科学版),2013,36(02):15.
　Guo Jinyong.The Existence of Weak Solutions for a Degenerate Pseudoparabolic Equation[J].Journal of Nanjing Normal University(Natural Science Edition),2013,36(01):15.
[5]李宇尘,张康群.一类Duffing方程周期解的存在唯一性[J].南京师大学报(自然科学版),2016,39(03):16.[doi:10.3969/j.issn.1001-4616.2016.03.003]
　Li Yuchen,Zhang Kangqun.The Existence and Uniqueness of Periodic Solution toa Class of Duffing Equations[J].Journal of Nanjing Normal University(Natural Science Edition),2016,39(01):16.[doi:10.3969/j.issn.1001-4616.2016.03.003]

备注/Memo

备注/Memo:
基金项目: 西安交通大学自然科学基金和国家自然科学基金资助项目( 10426027, 10571022) .
作者简介: 朱立平, 女, 1977- , 助教, 主要从事偏微分方程理论和数值计算的学习与研究.
通讯联系人: 张正策, 1976- , 博士, 主要从事偏微分方程理论的教学与研究. E-m ail:zhangzc@ m ail.xjtu. edu. cn
更新日期/Last Update: 2013-05-05