[1]穆罕麦德,沈尧天,姚仰新,等.带非齐次项和Sobolev-Hardy临界指数的奇异椭圆方程的多解(英文)[J].南京师大学报(自然科学版),2008,31(04):1-7.
　Ahamed Adam Abdelgadir,Shen Yaotian,Yao Yangxin.Multiple Solutions for Elliptic Equation With Critical Sobolev-Hardy Exponent and Inhomogeneous Term[J].Journal of Nanjing Normal University(Natural Science Edition),2008,31(04):1-7.
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带非齐次项和Sobolev-Hardy临界指数的奇异椭圆方程的多解(英文)()
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《南京师大学报（自然科学版）》[ISSN:1001-4616/CN:32-1239/N]

卷:
第31卷
期数:
2008年04期
页码:
1-7
栏目:
数学
出版日期:
2008-12-30

文章信息/Info

Title:
Multiple Solutions for Elliptic Equation With Critical Sobolev-Hardy Exponent and Inhomogeneous Term
作者:
穆罕麦德;沈尧天;姚仰新;
华南理工大学数学科学学院
Author(s):
Ahamed Adam Abdelgadir1; 2; Shen Yaotian1; Yao Yangxin1
1.School of Mathematical Sciences,South China University of Technology,Guangzhou 510640,China
2. B lue N ileU nivers ity, Facu lty ofE ngineering Departm en t ofMathem atics, Dam az in-Sudan
关键词:
p-阶拉普拉斯方程;  临界指数;  最佳常数;  Sobolev-Hardy不等式
Keywords:
p-Laplace equa tion;  cr itica l exponent;  best constant;  Sobo lev-H ardy inequality
分类号:
O175.25
摘要:
设2*=2(N+α)(N-2+β),N≥3,是极限Sobolev指数,ΩRN是RN中的开子集.在f(x)∈Hβ-1满足合适的条件且f(x)≠0下,讨论了一个带非齐次项和Sobolev-Hardy临界指数的含权的椭圆型问题:{-div(|x|β▽u)=|x|αup*-1+εf(x),x∈Ω,u>0,x∈Ω,u=0,x∈Ω,,存在两个解u和-u在H01,,βp(Ω)中,且有u≥0,u-≥0对所有的f(x)≥0.值得注意的是,当f(x)=0时一般不成立.

参考文献/References:

[ 1] BrezisH, N irenberg L. Positive so lutions o f nonlinear elliptic equation invo lv ing critica l Sobo lev exponents[ J]. Comm Pure App lM ath, 1983( 36) : 437-477.
[ 2] Cao D M, Zhou H S. On the ex istence of mu ltip le so lutions of no hom ogeneous e lliptic equations invo lv ing exponents[ J].ZAMP, 1996( 47): 89-96.
[ 3] Caffare lli L, Kohn R , N irenberg L. F irst order in terpolation inequa lities w ith w e ights[ J]. Com pos itioM a th, 1984( 53):259-275.
[ 4] B rezisH, Lieb E. A relation betw een po intw ise convergence o f func tions and convergence o f func tiona ls[ J]. ProcAm erM a th Soc, 1983, 88( 3): 486-490.
[ 5] Ghoussoub N, Yuan C. M u ltiplic so lu tions for quasilinea r PDEs invo lv ing the critical Sobo lev and H ardy exponents[ J].T rans Am e rM ath Soc, 2000, 352( 12): 5 703-5 743.

备注/Memo

备注/Memo:
Foundation item: Supported by the N at iona lS cien ce Foundat ion of Ch ina ( 10771074) .
Corresponding autho r: Aham ed Adam Abdelgad ir, doctoral student, m ajored in part ial d ifferen tial equat ion s. E-m ail:ahm edm ath17@ hotm ail.com
更新日期/Last Update: 2013-05-05