期刊文献+
任意字段
题名或关键词
题名
关键词
文摘
作者
第一作者
机构
刊名
分类号
参考文献
作者简介
基金资助
栏目信息

一类奇异半线性椭圆方程解的不存在性 被引量：1

Nonexistence of Solutions for a Singular Semilinear Elliptic Equation
原文传递
导出
摘要 研究了一类奇异半线性椭圆方程解的不存在性,改进并补充了Arcoya等人的一个研究工作[Existence and nonexistence of solutions for singular quadratic quasilinear equations,J Differential Equations,2009,246:4006-4042].本文使用的方法非常简单,证明过程中用到了Poincare等式,Lusin定理以及Egoroff定理. We study the nonexistence of solutions for a singular semilinear elliptic equations. The results improve and implement a work by Arcoya et al. IExistence and nonexistence of solutions for singular quadratic quasilinear equations, J. Differential Equations, 2009, 246： 4006-4042], whose proofs are very simple and based on Poincar~ inequality, Lusin theorem and Egoroff theorem.
作者 周文书 魏晓丹 秦绪龙
机构地区 大连民族学院理学院 中山大学数学与计算科学学院
出处 《数学学报（中文版）》 SCIE CSCD 北大核心 2014年第1期125-130,共6页 Acta Mathematica Sinica：Chinese Series
基金 国家自然科学基金项目(10901030 11001278) 中国博士后科研基金项目(20090450191) 中央高校基本科研业务费专项基金项目(DC110109 DC120101064)
关键词 奇异椭圆方程 不存在性 逼近问题 singular elliptic equation nonexistence approximation problem
分类号 O175.25 [理学—基础数学]
  • 相关文献

参考文献11

  • 1Arcoya D., Carmona J., Leonori T., et al., Existence and nonexistence of solutions for singular quadratic quasilinear equations, J. Differential Equations, 2009, 246: 4006-4042.
  • 2Arcoya D., Segura de Le6n S., Uniqueness of solutions for some elliptic equations with a quadratic gradient term, ESAIM Control Optim. Cal. Var., 2010, 16: 327-336.
  • 3Barenblatt G. I., Bertsch M., Chertock A. E., et al., Self-similar intermediate asymptotic for a degenerate parabolic filtration-absorption equation, Proc. Nat. Acad. Sci. USA, 2000, 97(18): 9844-9848.
  • 4Bertsch M., Ughi M., Positivity properties of viscosity solutions of a degenerate parabolic equation, Nonlinear Analysis TMA, 1990, 14: 571-592.
  • 5Boccardo L., Dirichlet problems with singular and gradient quadratic lower order terms, ESAIM Control Optim. Cal. Vat., 2008, 14: 411-426.
  • 6Chasseigne E., Vazquez J. L., The pressure equation in the fast diffusion range, Rev. Mat. Iberoamericana, 2003, 19(3): 873-917.
  • 7Fukuda I., Ishii H., Tsutsumi M., Uniqueness of solutions.to the Cauchy problem for ut -uAu q-:/[Vu[2 = 0, Differential Integral Equations, 1993, 6(6): 1231-1252.
  • 8Jiang Z. J., Wu Z. Q., Real Variable Function (2nd edition), Higher Education Press, Beijing, 1994 (in Chinese).
  • 9Porru G., Vitolo A., Problems for elliptic singular equations with a quadratic gradient term, J. Math. Anal. Appl., 2007, 334: 467-486.
  • 10Zhou W. S., A singular nonlinear elliptic equation with natural growth in the gradient, Math. Meth. Appl. Sci., 2008, 31: 1704-1721.

同被引文献8

  • 1Bensoussan A, Boccardo L, Murat F. On a Nonlinear Partial Differential Equation Having Natural Growth Terms and Unbounded Solution[J]. Ann Inst H Poincare Anal Non Lineairc , 1988, 5(4): 347-364.
  • 2Boccardo L, Gallouet T. Strongly Nonlinear Elliptic Equations Having Natural Growth Terms and L' Data[J]. Nonlinear Anal: Theory, Methods & Applications, 1992, 19(6): 573-579.
  • 3Arcoya D, Barile S, Mart inez-Apar icio PJ. Singular Quasilinear Equations with Quadratic Growth in the Gradient without Sign Condition[J].J Math Anal Appl , 2009, 350(1): 401-408.
  • 4Arcoya D, TapiaJ C, Martinez-Aparicio P 1. Elliptic Obstacle Problems with Natural Growth on the Gradient and Singular Nonlinear Terms[J]. Adv Nonlinear Stud, 2007, 7(2): 299-317.
  • 5Arcoya D, Martinez-Aparicio PJ. Quasilinear Equations with Natural Growth[J]. Rev Mat Iberoarnericana , 2008, 24(2): 597-616.
  • 6Figueiredo D G, de. Positive Solutions of Semilinear Elliptic Problems[M]/ /Differential Equations. Lecture Notes in Math, Vol. 957. Berlin: Springer-Verlag, 1981: 34-87.
  • 7Arcoya D, CarmonaJ, Leonori T, et al. Existence and Nonexistence of Solutions for Singular Quadratic Quasilinear Equations[J].J Differential Equations, 2009, 246(10): 4006-4042.
  • 8景元萍,郭斌,张永胜.一类具奇异项和梯度项的拟线性椭圆方程正解的不存在性[J].吉林大学学报（理学版）,2012,50(5):969-971. 被引量：1

引证文献1

数学学报（中文版）
2014年 第1期

相关作者

内容加载中请稍等...

相关机构

内容加载中请稍等...

相关主题

内容加载中请稍等...

浏览历史

内容加载中请稍等...
;
使用帮助 返回顶部