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H^1(R^N)上带限制的椭圆特征问题的三个解 被引量：4

Three Solutions of an Elliptic Eigenvalue Problem with Constraint in H^1(R^N)
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摘要 用变分方法证明H^1(R^N)上一个带限制的半线性椭圆特征问题解的存在性.所获得的三个解:一个是正解,一个是负解.对于第三个解,本文只证明了它的存在性,而没有确定它是正解,负解,还是变号解. This paper proves the existence of three solutions of a semilinear elliptic eigen- value problem in H1 （RN） with constraint by using variational methods. One is a positive solution; anther one is a negative solution; the third one is not fixed.
作者 刘竞坤
机构地区 集美大学诚毅学院
出处 《数学研究》 CSCD 2013年第2期160-166,共7页 Journal of Mathematical Study
关键词 椭圆特征问题 临界点理论 多解 Elliptic eigenvalue problem Critical point theory Multiple solutions
分类号 O175.25 [理学—基础数学]
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参考文献13

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同被引文献13

  • 1KRYSZEWSKI W, SZULKIN A. Generalized linking theorem with an application to semilinear Schrodinger equation. Advdiff eq, 1998, 3(3) : 441-472.
  • 2LIU J K, CHEN J Q. Sign changing solutions and multiple solutions of an elliptic eigenvalue problem with constraint in//' ( RN ) ? Computers and mathematics with applications, 2010,59(8) : 3005-3013. 019.
  • 3REED M,SIMON B. Methods of modem mathematical physics IV. New York: Academic Press,1978 : 309-310.
  • 4ZELATI V C,RABINOWITZ P H. Homoclinic type solutions for a semilinear elliptic PDE on R' Comm pure appl math,1992(45) : 1217-1269.
  • 5MAWHIN J, WILLEM M. Critical point theory and hamiltonian system. New York: Springer-Verlag, 1989: 175-176.
  • 6GILBARG D, THUDINGER N S. Elliptic partial differential equations of second order. New York: Springer-Verlag,1977: 32-35.
  • 7WILLEM M. Minimax theorems. Berlin: Birkhauser Boston Basel, 1996: 93-107.
  • 8RABINOWITZ P H. Minimax methods in critical point theory with applications to differential equations. Providence :Amer Math Soc, 1986 : 1-22.
  • 9姜兆敏.常微分方程初值问题的变分迭代算法[J].长春工业大学学报,2013,34(1):9-12. 被引量：3
  • 10刘竞坤.H^1(R^N)上一类半线性椭圆问题的正解与负解[J].集美大学学报（自然科学版）,2016,21(3):228-233. 被引量：3

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数学研究
2013年 第2期

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