中国综合性科技类核心期刊(北大核心)

中国科学引文数据库来源期刊(CSCD)

美国《化学文摘》(CA)收录

美国《数学评论》(MR)收录

俄罗斯《文摘杂志》收录

留言板

尊敬的读者、作者、审稿人, 关于本刊的投稿、审稿、编辑和出版的任何问题, 您可以本页添加留言。我们将尽快给您答复。谢谢您的支持!

姓名
邮箱
手机号码
标题
留言内容
验证码

带临界指数的奇异椭圆方程Neumann问题多重解的存在性

陈自高

陈自高. 带临界指数的奇异椭圆方程Neumann问题多重解的存在性[J]. 华东师范大学学报(自然科学版), 2011, (5): 79-87.
引用本文: 陈自高. 带临界指数的奇异椭圆方程Neumann问题多重解的存在性[J]. 华东师范大学学报(自然科学版), 2011, (5): 79-87.
CHEN Zi-gao. Existence of multiple solutions for singular elliptic equations involving critical exponents with Neumann boundary condition[J]. Journal of East China Normal University (Natural Sciences), 2011, (5): 79-87.
Citation: CHEN Zi-gao. Existence of multiple solutions for singular elliptic equations involving critical exponents with Neumann boundary condition[J]. Journal of East China Normal University (Natural Sciences), 2011, (5): 79-87.

带临界指数的奇异椭圆方程Neumann问题多重解的存在性

详细信息
  • 中图分类号: O175.25

Existence of multiple solutions for singular elliptic equations involving critical exponents with Neumann boundary condition

  • 摘要: 利用变分法, 在n维空间有界区域上, 研究了一类含有Sobolev-Hardy临界指数与Hardy项的奇异椭圆方程Neumann 问题弱解的存在性和多重性. 在f(x,t)满足非二次条件的情况下, 运用对偶喷泉定理与拉直边界的方法, 证明了存在*0使得当(0,*)时, 该问题存在无穷多个具有负能量的弱解{u_k} 被包含于W^{1,2}()并且当k时, J(u_k)0.
  • [1] {1}WANG X. Neumann problems of semilinear elliptic equations involving critical Sobolev exponents [J]. J Diff Eq, 1991, 93: 283-310.
    {2}GHOUSSOUB N, KANG X S. Hardy-Sobolev critical elliptic equations with boundary singularities [J]. Ann Inst H Poincare-AN, 2004, 21(6): 767-793.
    {3}商彦英, 唐春雷. 一类奇异椭圆方程无穷多解的存在性[J]. 东北师大学报:自然科学版, 2007, 39(4): 10-16.\\

    SHANG Y Y, TANG C L. Existence of infinitely many solutions for some singular elliptic equation [J]. Journal of Northeast Normal University: Natural Science Edition, 2007, 39(4): 10-16.
    {4}龚亚英. 含有Sobolev-Hardy临界指数的拟线性椭圆方程解的存在性和多重性[J]. 数学杂志, 2009, 29(4): 500-504.\\

    GONG Y Y. Existence and multiplicity results for some quasilinear elliptic equation with critical Sobolev-Hardy exponent [J]. J Math (PRC), 2009, 29(4): 500-504.
    {5} 商彦英, 唐春雷. 含有Sobolev-Hardy临界指数的椭圆方程解的存在性和多重性[J]. 兰州大学学报:自然科学版, 2007, 43(4): 121-126.\\

    SHANG Y Y, TANG C L. Existence of and multiplicity for some elliptic equations with critical Sobolev-Hardy exponent [J]. Journal of Lanzhou University: Natural Sciences, 2007, 43(4): 121-126.
    {6} 胡爱莲, 张正杰. 含有Sobolev-Hardy临界指标的奇异椭圆方程Neumann问题无穷多解的存在性[J]. 数学物理学报, 2007, 27A(6): 1025-1034. \\                                          HU A L, ZHANG Z J. The existence of infinitely many solutions for an elliptic equation involving critical Sobolev-Hardy exponent with Neumann boundary condition [J]. Acta Math Scientia, 2007, 27A(6): 1025-1034.
    {7} CAO D, NOUSSAIR E S. The effect of gemometry of the domain boundary in an elliptic Neumann problem [J]. Adv Diff Eq, 2001, 6(8): 931-958.
    {8} HAN P G, LIU Z. Positive solutions for elliptic equations involving the critical Sobolev exponents and Hardy terms with Neumann boundary conditions [J]. Nonlinear Anal, 2003, 55: 167-186.
    {9} WANG X. Neumann problems of semilinear elliptic equations involving critical Sobolev exponents [J]. J Diff Eq, 1991, 93: 283-310.
    {10} HAN P G. Neumann problems of a class of elliptic equations with doubly critical Sobolev exponents [J]. Acta Math Scientia, 2004, 24B(4): 633-638.
    {11} COMTE M, KNAAP M C. Existence of solutions of elliptic equations involving critical Sobolev exponents with Neumann boundary conditions in general domains [J]. Diff Integral Eq, 1991, 4: 1133-1146.
    {12} BARTSCH T, WILLEM M. On an elliptic equation with concave and convex nonlinearility [J]. Proc Amer Math Soc, 1995, 123: 3555-3561.
    {13} WILLEM M. Minmax theorems [M]. Boston: Birkh\"{a}uhser, 1996.
    {14} GHOUSSOUB N, YUAN C. Multiple solutions for a quasilinear PDEs involving the critical Sobolev-Hardy exponents [J]. Trans Amer Math Soc, 2000, 352(12): 5703-5743.
    {15} 王征平, 阮立志. 含有Sobolev-Hardy临界指标的奇异椭圆方程无穷多解的存在性[J]. 应用数学, 2004, 17(4): 639-648.\\

    WANG Z P, RUAN L Z. The existence of infinitely many solutions for a singular elliptic equation involving critical Sobolev-Hardy exponent [J]. Math Appl, 2004, 17(4): 639-648.
  • 加载中
计量
  • 文章访问数:  2380
  • HTML全文浏览量:  10
  • PDF下载量:  216
  • 被引次数: 0
出版历程
  • 收稿日期:  2011-03-01
  • 修回日期:  2011-06-01
  • 刊出日期:  2011-09-25

目录

    /

    返回文章
    返回