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

奇异扰动的p-Laplace方程非负非平凡解和正解的结构

张正策 李开泰

张正策, 李开泰. 奇异扰动的p-Laplace方程非负非平凡解和正解的结构[J]. 应用数学和力学, 2004, 25(8): 847-854.
引用本文: 张正策, 李开泰. 奇异扰动的p-Laplace方程非负非平凡解和正解的结构[J]. 应用数学和力学, 2004, 25(8): 847-854.
ZHANG Zheng-ce, LI Kai-tai. Structure of Nonnegative Nontrivial and Positive Solutions of Singularly Perturbed p-Laplace Equations[J]. Applied Mathematics and Mechanics, 2004, 25(8): 847-854.
Citation: ZHANG Zheng-ce, LI Kai-tai. Structure of Nonnegative Nontrivial and Positive Solutions of Singularly Perturbed p-Laplace Equations[J]. Applied Mathematics and Mechanics, 2004, 25(8): 847-854.

奇异扰动的p-Laplace方程非负非平凡解和正解的结构

基金项目: 国家重点基础研究专项基金资助项目(1999032801);国家自然科学基金资助项目(10371095)
详细信息
    作者简介:

    张正策(1976- ),男,河南邓州人,讲师,博士,主要从事偏微分方程理论研究(联系人.Tel:+86-29-82671775;E-mail:zhangzc@mail.xjtu.edu.cn).

  • 中图分类号: O175.25

Structure of Nonnegative Nontrivial and Positive Solutions of Singularly Perturbed p-Laplace Equations

  • 摘要: 精确地刻画了某些奇异扰动的p-Laplace方程非负非平凡解和正解的结构.利用上下解方法证明,方程存在很多非负非平凡的尖峰解和正的过渡尖峰解.当参数充分小时还对每个尖峰解支集的上下界进行了估计.
  • [1] Diaz J I.Nonlinear Partial Differential Equation and Free Boundaries—Ⅰ:Elliptic Equations[M].London:Pitman,1985.
    [2] 杨作东,陆启韶.一类非牛顿渗流系统爆破界的估计[J]. 应用数学和力学,2001,22(3):287—294.
    [3] 白占兵.一类四阶p-Laplace 方程正解的存在性及多解性[J].应用数学和力学, 2001,22(12):1324—1328.
    [4] Guo Z M, Webb J R L, Large and small solutions of a class of quasilinear elliptic eigenvalue problems[J].J Differential Equations,2002,180(1):1—50.
    [5] ZHANG Zheng-ce, LI Kai-tai.Spike-layered solutions of singularly perturbed quasilinear Dirichlet problems[J].J Math Anal Appl,2003,283(2):667—680. doi: 10.1016/S0022-247X(03)00333-0
    [6] Dancer E N, Wei J C.On the profile of solutions with two sharp layers to a singularly perturbed semilinear Dirichlet problem[J].Proc Roy Soc Edinburgh Sect A,1997,127(4):691—701. doi: 10.1017/S0308210500023775
    [7] Ni W M, Takagi I, Wei J C.On the location and profile of spike-layer solutions to a singularly perturbed semilinear Dirichlet problems: Intermediate solutions[J].Duke Math J,1998,94(3):597—618. doi: 10.1215/S0012-7094-98-09424-8
    [8] Dancer E N, Wei J C.On the location of spikes of solutions with two sharp layers for a singularly perturbed semilinear Dirichlet problem[J].J Differential Equations,1999,157(1):82—101. doi: 10.1006/jdeq.1998.3619
    [9] Vzquez J L.A strong maximum principle for some quasilinear elliptic equations[J].Appl Math Optim,1984,12(3):191—202. doi: 10.1007/BF01449041
    [10] Diaz J I, Herrero M A.Estimates on the support of the solutions of some nonlinear elliptic and parabolic problems[J].Proc Roy Soc Edinburgh Sect A,1981,89(2):249—258. doi: 10.1017/S0308210500020266
    [11] Gidas B, Ni W M,Nirenberg L.Symmetry and related properties via the maximum principle[J].Comm Math Phys,1979,68(3):209—243. doi: 10.1007/BF01221125
    [12] Brock F.Continuous rearrangement and symmetry of solutions of elliptic problems[J].Proc Indian Acad Sci Math Sci,2000,110(2):157—204. doi: 10.1007/BF02829490
    [13] Brock F.Radial symmetry for nonnegative solutions of semilinear elliptic equations involving the p-Laplacian[A,J]. In:Amann H,Bandle C,Chipot M,et al Eds.Progress in Partial Differential Equations[C].Vol 1.Pont--Mousson 1997,1—12;Pitman Res Notes Math Ser,Harlow-New York:Longman, 1998,383:46—58.
    [14] ?tani M, Teshima T. On the first eigenvalue of some quasilinear elliptic equations[J]. Proc Japan Acad Ser A,1988,64(1):8—10. doi: 10.3792/pjaa.64.8
    [15] Guo Z M.Structure of nontravial nonnegative solutions to singularly perturbed semilinear Dirichlet problems[J].Proc Roy Soc Edinburgh Sect A,2003,133(2):363—392. doi: 10.1017/S0308210500002432
    [16] Caada A, Drbek P, Gamez J L. Existence of positive solutions for some problems with nonlinear diffusion[J].Trans Amer Math Soc,1997,349(10):4231—4249. doi: 10.1090/S0002-9947-97-01947-8
    [17] Guo Z M.Uniqueness and flat core of positive solutions for quasilinear elliptic eigenvalue problems in general smooth domains[J].Math Nachr,2002,243(1):43—74. doi: 10.1002/1522-2616(200209)243:1<43::AID-MANA43>3.0.CO;2-U
    [18] Guo Z M. Structure of large positive solutions of some semilinear elliptic problems where the nonlinearity changes sign[J].Top Methods Nonlinear Anal,2001,18(1):107—128.
  • 加载中
计量
  • 文章访问数:  2979
  • HTML全文浏览量:  146
  • PDF下载量:  688
  • 被引次数: 0
出版历程
  • 收稿日期:  2002-11-05
  • 修回日期:  2004-03-08
  • 刊出日期:  2004-08-15

目录

    /

    返回文章
    返回