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求解非线性椭圆型方程边值问题的分歧方法 被引量：5

Bifurcation method for solving boundary value problems of nonlinear elliptic PDE's
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摘要 用对称破缺分歧理论的方法计算了非线性椭圆型方程边值问题的多个解,讨论了非平凡解的各种对称性质,画出了从各个分歧点出发的具有各种对称性质的解. The theory and algorithm of symmetry-breaking bifurcation are applied to finding multiple solutions for boundary value problems of nonlinear elliptic PDE's, different symmetry properties of nontrivial solutions have been studied, and numerical multiple solutions which have vary symmetry properties bifurcating from bifurcation points are visualized.
作者 杨忠华 李业忠
机构地区 上海师范大学数理信息学院
出处 《上海师范大学学报（自然科学版）》 2005年第2期17-20,共4页 Journal of Shanghai Normal University(Natural Sciences)
基金 上海市科委科技发展基金(No.00JC14057)(No.03QA14036).
关键词 非线性椭圆型方程 多解 对称破缺 分歧 L-S方法 nonlinear elliptic equation multiple solutions symmetry-breaking bifurcation Liapunov-Schmidt reduction
分类号 O175 [理学—基础数学]
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参考文献4

  • 1ZHONGHAI DING, DAVID COSTA ,GOONG CHEN. A high-linking algorithm for sign-changing solutions of semilinear elliptic equations[J]. Nonlinear Anal , 1999, 38 : 151 - 172.
  • 2P H RABINOWITZ. Minimax methods in critical point theory with applications to differential equations [J]. Conf Board Math Sci Reg Conf Ser Math ,1986 ,65:1 -44.
  • 3Y S CHOI, P J MCKENMA. Mountian pass method for the numerical solution of semilinear elliptic problems [J]. Nonlinear Anal ,1993 ,20:417 -437.
  • 4GOONG CHEN, JIANXIN ZHOU, WEI - MING NI. Algorithms and visualization for solutions of nonlinear elliptic equations [J]. International Journal of Bifurcation and Chaos ,2000,10 (7): 1565 - 1612.

同被引文献16

  • 1Shuang-jie Peng.Multiple Boundary Concentrating Solutions to Dirichlet Problem of Hénon Equation[J].Acta Mathematicae Applicatae Sinica,2006,22(1):137-162. 被引量：4
  • 2李昭祥,杨忠华,朱海龙,沈建.Henon方程多解计算的分歧方法[J].上海师范大学学报（自然科学版）,2007,36(1):1-6. 被引量：4
  • 3[1]Choi Y S,Mckenna P J.A mountain pass method for the numerical solutions of semi-inare elliptic problems[J].Nonlinear Anal,1993,20:417-437.
  • 4[2]Ding Z H,Costa D,Chen G.A high-linking algorithm for sign-changing solutions of semi-linear elliptic equations[J].Nonlinear Anal,1999,38:151-172.
  • 5[3]Li Y,Zhou J X.A minimax method for finding multiple critical points and its application to semi-linear PDEs[J].SLAM J Sci Comput,2002,23:840-865.
  • 6CHOIYSMCKENNA P J.A Mountian pass method for the numerical solution of semilinear elliptic problem[J].Nonlinear Anal,1993,20(4):417-437.
  • 7DING Zhonghai,COSTA David,CHEN Goong.A high-linking algorithm for sign-changing solution of semilinear elliptic equation[J].Nonlinear Anal,1999,38(2):151-172.
  • 8LI Y,ZHOU J X.A minimax method for finding multiple critical points and its application to semi-linear PESs[J].SIAM J Sci Comput,2002,23(3):840-865.
  • 9YAO X D,ZHOU J X.A minimax method for finding multiple critical points in Banach spaces and application to quasilinear elliptic PDE[J].SIAM J Sci Comput,2005,26(5):1 796-1 809.
  • 10CHEN C M,XIE Z Q.Search-extension method for multiple solution of nonlinear problem[J].Comp Math Appl,2004,47(2):327-343.

引证文献5

二级引证文献6

上海师范大学学报（自然科学版）
2005年 第2期

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