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一类非线性椭圆型方程边值问题解的有界性 被引量：2

The Bounded Solutions to the Boundary Value Problem of a Class of Nonlinear Elliptic Equations
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摘要 研究一类含有参数λ的非线性椭圆型方程边值问题:-Δu=λf(|x|,u),x∈Ω,u=0,x∈-Ω,得到了边值问题解的有界性定理. In this paper, the boundary value problems of nonlinear elliptic equations with a parameter λ {-Δu=λf（｜x｜,u）,u=0,x∈Ω,x∈Ω are studied and the bounded theorems of the boundary value problems are obtained.
作者 许兴业
机构地区 广东教育学院数学系
出处 《广东教育学院学报》 2006年第3期19-22,共4页 Journal of Guangdong Education Institute
基金 广东教育学院教授博士专项经费资助项目
关键词 边值问题 参数λ 足够光滑 HOELDER连续 有界性 boundary value problem parameter λ； smooth enough； Hoelder continuous bound
分类号 O175.25 [理学—基础数学]
  • 相关文献

参考文献8

  • 1SEIDMAN T I. The asymptotic growth of solutions of -△u=λf(u) for large λ[J]. Indiana Univ Math J, 1981,30:305-311.
  • 2许兴业.一类非线性椭圆型方程解的存在惟一性[J].广东教育学院学报,2005,25(3):21-23. 被引量：3
  • 3许兴业.一类非线性椭圆型方程的解关于λ的可微性[J].广东教育学院学报,2005,25(5):24-26. 被引量：1
  • 4SCHUHMAN V. About uniqueness for nonlinear boundary value problems[J]. Math Ann, 1984,267:537-542.
  • 5NOUSSAIR E S, SWANSON C A. Global positive solutions of semilinear elliptic problems[J]. Pacific J Math, 1984,115 : 177-192.
  • 6ANGENENT S B. Uniqueness of the solution of simelinear boundary value problem[J]. Math Ann,1985,272:129-138.
  • 7WEIGNER M. A uniqueness theorem for some nonlinear boundary value problems with a large parameter[J]. Math Ann, 1984 , 270 :401-402.
  • 8DANCER E N. On the number of positive solutions of weakly nonlinear elliptic equations with a parameter is large[J]. Proc London Math Soc, 1986, 53:429-452.

二级参考文献17

  • 1许兴业.一类非线性椭圆型方程解的存在惟一性[J].广东教育学院学报,2005,25(3):21-23. 被引量：3
  • 2SCHUHMAN V. About uniqueness for nonlinear boundary value problems[J]. Math Ann, 1984,267:537-542.
  • 3NOUSSAIR E S, SWANSON C A. Global positive solutions of semilinear elliptic problems[J]. Pacific J Math, 1984,115:177- 192.
  • 4ANGENENT S B. Uniqueness of the solution of simelinear boundary value problem[J]. Math Ann,1985,272: 129-138.
  • 5WEIGNER M. A Uniqueness theorem for some nonlinear boundary value problems with a large parameter[J]. Math Ann, 1984, 270: 401-402.
  • 6DANCER E N. On the number of positive solutions of weakly nonlinear elliptic equations with a parameter is large[J]. Proc London Math Soc, 1986,53: 429-452.
  • 7SEIDMAN T I. The asymptotic growth of solutions of -Au=λf(u) for large λ [J]. Indiana Univ Math J, 1981,30:305-311.
  • 8GILBARY D, TRUDINGER N S. Elliptic partial differential equations of second order[M]. New York Tokyo: Springer - Verlag, 1983. 33.
  • 9H. Aman, On the existence of positive solutions of nonlinear elliptic boundary value problems[J].Indiana Univ Math J, 1971,21:125-146.
  • 10SCHUHMAN V. About uniqueness for nonlinear boundary value problems[J]. Math Ann, 1984,267:537-542.

共引文献2

同被引文献9

  • 1桂贵龙,田立新.Dullin-Gottwald-Holm方程解的极限行为[J].江苏大学学报（自然科学版）,2005,26(B12):10-14. 被引量：1
  • 2胡爱莲.四阶非线性微分方程解的有界性及稳定性[J].内蒙古师范大学学报（自然科学汉文版）,2006,35(1):26-29. 被引量：4
  • 3Klaus Weihrauch,Zhong Ning. Computing the solution of the Korteweg-de Vries equation with arbitrary precision on Turing machines[J]. Theoretical Computer Science, 2005,332(1-3) : 337-366.
  • 4Abdul-Majid Wazwaz. Kinks and solitions solutions for the Combined KdV equation with two power non- linearities[J]. Applied Math and Computation,2006,183(2) :1181-1189.
  • 5Weihrauch K. Computable Analysis[M]. Berlin:Springer,2000.
  • 6Zhong Ning,Weihraueh K. Computability theory of generalized functions[J]. Jassoc, for Computing Machinery, 2003,50(4): 469-505.
  • 7WAZWAZ A M. Kinks and solitions solutions for the Generalized KdV equation with two power nonlineari- ties[J]. Applied Math and Computation, 2006, 183 (2) : 1181-1189.
  • 8WEIHRAUCH K, ZHONG Ning. Computing the so lution of the Korteweg-de Vries equation with arbitrar- y precision on Turing maehines[J]. Theoretical Com- puter Science, 2005, 332(1/2/3): 337-366.
  • 9LU Dianchen, WANG Qingyan. Computing the solu- tion of the m-Korteweg-de Vries equation on Turing machines[J]. Electronic Notes in Theoretical Comput- er Science, 2008, 202(3): 219-236.

引证文献2

广东教育学院学报
2006年 第3期

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