[1]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].南京师范大学学报(自然科学版),2006,29(01):21-24.
 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):21-24.
点击复制

一类拟线性椭圆型方程正奇异解的能量估计()
分享到:

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

卷:
第29卷
期数:
2006年01期
页码:
21-24
栏目:
数学
出版日期:
2006-03-30

文章信息/Info

Title:
Energy Estimate of Positive Singular Solutions for a Class Quasilinear Elliptic Equations
作者:
周杰 杨作东
南京师范大学数学与计算机科学学院, 江苏南京210097
Author(s):
Zhou JieYang Zuodong
School of Mathematics and Computer Sciences,Nanjing Normal University,Nanjing 210097,China
关键词:
存在性 正奇异解 拟线性椭圆型方程 能量估计
Keywords:
existence po sitive singular so lution quas ilinear e lliptic equa tion energy estimate
分类号:
O175.25
摘要:
本文给出了如下问题d iv(|u|p-2 u)+λf(u)=0,x∈Ωu|Ω=0,奇异解的能量估计,其中p≥2,Ω=B1是单位球,λ>0是一个参数.进一步得到了uλ是上述问题的正则正解序列且当λ→λ0∈(0,∞)时逐点收敛于奇异解U,则在Lq+1(B1)和H01(B1)中,当λ→λ0时uλ收敛于U.
Abstract:

参考文献/References:

[ 1] L in S S. Positive singular solution for sem ilinear e lliptic equations w ith supercr itica l g row th[ J]. J D iff Eqns, 1994, 114( 1): 57- 76.
[ 2] Guedda M, Veron L. Lo ca l and g loba l prope rties o f so lutions of quasilinear e lliptic equa tions [ J]. J Diff Eqns, 1988, 76( 1): 159- 189.
[ 3] Q i Jiangang, ZhuangW an. Ex istence of singu la r positive solutions of sem ilinear elliptic equations[ J]. ActaM a th App licate S in ica, 1998, 14( 1): 109- 112.
[ 4] N iW M, Serrin J. Nonex istence theo rem s fo r singu la r solutions o f quas ilinear partia l d iffe rentia l equations[ J]. Comm Pure ApplM ath, 1986, 39: 379-399.
[ 5] Ga lloue t T, M ignot F, Pue l J P. Que lques resu ltas su r le problem e ( u =λ eu [ J]. C R Acad Sc i Paris Ser IM ath, 1988, 307: 282- 292.
[ 6] 杨作东. 一类拟线性椭圆型方程正奇异解的存在性[ J] . 数学物理学报, 2005, 25A ( 4): 445- 450.
[ 7] Yang Zuodong. Ex istence o f positive bounded entire so lutions o f quasilinear ellip tic equa tions[ J]. App liedM ath and Com pu tation, 2004, 156( 3): 743-754.
[ 8] Y ang Zuodong, Guo Zongm ing. Ex istence of pos itive rad ia l so lu tions and entire so lutions for quasilinear singu la r boundary value prob lem s[ J]. Ann of D iff Eqns, 1996, 12( 2): 243- 251.
[ 9] Guo Zongm ing. Som e ex istence and m ultip lic ity resu lts for a class of quasilinear elliptic equations[ J]. Non linear Anal, 1992, 18( 10): 957-971.
[ 10] Guo Zongm ing, W ebb J R L. Un iqueness of positive so lutions for quasilinear e lliptic equations when a param eter is la rge [ J]. Proc Roy Soc Ed inburgh, 1994, 124A( 1): 189- 198.
[ 11] Garcia H u idobro M, M anasev ich, Y arur C S. On positive singu lar so lutions for a class of nonhomogeneous p La lacian Like equa tions[ J]. J D iff Eqns, 1998, 145( 1) : 23- 51.

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].南京师范大学学报(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]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].南京师范大学学报(自然科学版),2006,29(01):25.
 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.
[3]张康群,孙福树,赵国俊.一类半线性Keldysh型方程解的注记[J].南京师范大学学报(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].南京师范大学学报(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].南京师范大学学报(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: 国家自然科学基金( 10571022)和江苏省教育厅自然科学基金资助项目( 04K JB110062) .
作者简介: 周杰, 1981- , 硕士研究生, 主要从事微分方程方向的学习与研究.
通讯联系人: 杨作东, 1961- , 教授, 博士生导师, 主要从事微分方程方向的教学与研究. E mail:yangzuodong@ n jnu. edu. cn
更新日期/Last Update: 2013-05-05