一个带Hardy项的椭圆方程的多重解(英文)
Multiple Solutions for a Nonlinear Elliptic Equation with Hardy Term
摘要
通过对偶变分方法证明了一个带Hardy项和临界非线性的非线性椭圆方程的非平凡解的存在性和多重性.
Via dual variational principle, we show the existence and multiplicity of nontrivial solutions for a nonlinear elliptic equations with Hardy term and critical nonlinearity.
出处
《应用泛函分析学报》
CSCD
2006年第4期319-323,共5页
Acta Analysis Functionalis Applicata
参考文献11
-
1Ambrosetti A,Brezis H,Cerami G.Combined effects of concave and convex nonlinearities in some elliptic problems[J].Functional Analysis,1994,122:519-543.
-
2Ambrosetti A,Garcia J,Peral I.Multiplicity results for some nonlinear elliptic equations[J].Functional Analysis,1996,137:219-242.
-
3Chen J Q.Multiple positive solutions for a class of nonlinear elliptic equation[J].Math Anal Appl,2004,295:341-354.
-
4Chen J Q.Some further results on a semilinear equation with concave-convex nonl1inearity[J].Nonlinear Analysis,TMA,2005,62:71-87.
-
5Ferrero A,Gazzola F.Existence of solutions for singular critical growth semilinear elliptic equations[J].Differential Equations,2001,177:194-522.
-
6Jannelli E.The role played by space dimension in elliptic critical problems[J].Differential Equation,1999,156:407-426.
-
7Catrina F,Wang Z Q.On the Caffarelli-Kohn-Nirenberg inequalities:sharp constants,existence (and nonexistence) and symmetry of extremal functions[J].Comm Pure Appl Math,2001,56:229-258.
-
8Terracini S.On positive entire solutions to a class of equations with singular coefficient and critical exponent[J].Adv Diff Equa,1996,1(2):241-264.
-
9Brezis H,Lieb E.A relation between pointwise convergence of functions and convergence of functionals[J].Proc Amer Math Soc,1983,88:486-490.
-
10Ambrosetti A,Rabinowitz P.Dual variational methods in critical point theory and applications[J].Functional Analysis,1973,14:349-381.
-
1丁凌,周良金,张丹丹.在混合边界条件下临界指数椭圆方程的解[J].四川师范大学学报(自然科学版),2011,34(4):521-527. 被引量:4
-
2康东升,喻晶,王妹,曹玉平.带有临界Hardy-Sobolev指数和凸凹非线性项的(英文)[J].中南民族大学学报(自然科学版),2014,33(1):106-112.
-
3沈慧,王桂云,沈自飞.一类具临界指数的分数阶拉普拉斯方程对称解的存在性[J].浙江师范大学学报(自然科学版),2015,38(4):379-386. 被引量:2
-
4张端智.Maslov型指标及非线性Hamilton系统中的闸轨道[J].中国科学(A辑),2007,37(3):301-311.
-
5康东升,刘殊,黄燕.带有临界Hardy-Sobolev指数且含多个Hardy奇异项的非齐次椭圆方程解的存在性[J].中南民族大学学报(自然科学版),2009,28(2):104-108. 被引量:1
-
6石仁淑.一类一维临界非线性薛定谔方程组解的渐近行为[J].延边大学学报(自然科学版),2015,41(3):196-198. 被引量:1
-
7张桂宜,沈尧天.具临界指数和临界非线性边界条件的拟线性椭圆型方程Neumann问题[J].数学学报(中文版),1998,41(4):851-858. 被引量:2
-
8李科强.用指标理论对凸哈密顿系统周期解的一个存在性定理的推广[J].南京师大学报(自然科学版),2011,34(1):12-18.
-
9谌凤霞,何小飞.一类带调和势的临界非线性Schrdinger方程解的性质[J].数学学习与研究,2016(11):118-119.
-
10朱世辉,张健.关于带调和势的非线性Schrdinger方程的爆破解[J].四川大学学报(自然科学版),2009,46(5):1251-1256.