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

一类临界双调和方程正解的存在性

The Nontrivial Solutions of a Sort of Critical Biharmonic Equation
原文传递
导出
摘要 利用Sobolev-Hardy不等式和山路引理给出了一类带奇异系数和临界指数的双调和椭圆型方程△2u-μu/|x|2=u2*-1u+λur-1/|x|su,u>0,x∈Ω;u=0,x∈■Ω非平凡解的存在性结果. In this paper, the existence of biharmonic problem with sub-critical exponent and singular coefficient △^2u-μu/｜x｜2=μ^2＊-1^u＋λu^r-1/｜x^s｜u are proved by using the mountain passtheorem and Sobolev--Hardy inequality.
作者 张玉灵 何俊
机构地区 郑州升达经贸管理学院共科部
出处 《数学的实践与认识》 CSCD 北大核心 2013年第18期257-261,共5页 Mathematics in Practice and Theory
基金 国家自然科学基金(60872043)
关键词 Sobolev—Hardy不等式 双调和方程 临界指数 奇异系数 sobolev-hardy inequality biharmonic problem critical exponent singular coefficient
分类号 O175.25 [理学—基础数学]
  • 相关文献

参考文献8

  • 1王梅,姚仰新.一类椭圆型方程的非平凡解的存在性[J].深圳大学学报（理工版）,2004,21(4):359-362. 被引量：2
  • 2姚仰新,谢朝东.包含临界指数的奇异系数的椭圆型方程正解的存在性[J].华南理工大学学报（自然科学版）,2003,31(8):42-44. 被引量：4
  • 3Garcia AzoreroJ,Peral Alonso I.,Hardy inequalities and some critical elliptic and parabolic prob- lems[J]. Diff Equs, 1998, 144: 441-476.
  • 4Caffarelli L, Kohn R, lrenberg L. First order interpolation inequality with weights[J]. Comp Math, 1984, 53: 259-275.
  • 5RAAdams.索伯列夫空间[M].人民教育出版社,1983..
  • 6ChaudhuriN.带奇异系数的半线性的椭圆型方程的正解的存在性[J].爱丁堡皇家学会学报,2001,131A:1275-1295(英文版).
  • 7Edmunds D E, Fortunato D, Jannelli E. Critical exponents, critical dimensions and the biharmonic operator[J], Arch Rational Mech, Anal, 1990, 112: 269-289.
  • 8Filippo Gazzola, Hans-Christoph Grunau and Marco Squassina. Existence and nonexistence results for critical growth biharmonic elliptic equations[J]. Calc Var Partial Differential Equations, 2003, 18(2): 117-143.

二级参考文献13

  • 1[1]Ghoussoub N,Yang G. Multiple solutions for quasilinear PDEs involving the critical Sobolev and Hardy exponents[J]. Trans Amer Math Soc,2000,352(12):5703-5743.
  • 2[2]Chaudhuri N. Existence of positive solutions of some semilinear elliptic equations with singular coefficients[J].Proceding of the Royal Society of Edinburgh,2001,131A:1275-1295.
  • 3[3]Lions P L.The concentration-compactness principle in the calculus of variations,the limit case,part 1[J].Rev Mat Ibero,1985,1:541-597.
  • 4[4]Lions P L.The concentration-compactness principle in the calculus of variations,the limit case,part 1[J].Rev Mat Ibero,1985,1:45-121.
  • 5[5]Abdellaoui B,Pearl I. Some results for semilinear elliptic equations with critical potential[J].Proceding of the Royal Society of Edinburgh,2002,132A:1-24.
  • 6[6]Brezis H,Nirenberg L.Positive solutions of nonlinear elliptic equation invoving critical Sobolev exponents[J].Comm Pure Appl Math,1983,36:437- 477.
  • 7[7]Goncalves J V,Miyagaki O H. Multiple positive solutions for semilinear elliptic equation in R involving subcritical exponents[J]. Nonlinear Anal,1998,32(1):41-51.
  • 8[8]SHEN Yao-tian,YAN Shu-sen. The Calculus of Variations on Quasilinear Elliptic Equations[M].Guangzhou:Press of South China University of Technology,1995(in Chinese).
  • 9Chaudhuri N. Existence of positive solutions of some semilinear elliptic equations with singular coefficients [ J].Proc Roy Soc Edinb See,2001,131 :1 275 - 1 295.
  • 10Jannelli E. The role played by space dimension in elliptic critical problems [ J]. J Partial Equation, 1999,156(2) :407 - 426.

共引文献6

数学的实践与认识
2013年 第18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