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计算圆域上p-Henon方程边值问题多个正解的分歧方法 被引量：2

Bifurcation Method for Solving Multiple Positive Solutions to Boundary Value Problem of p-Henon Equation on the Unit Disk
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摘要 首先应用分歧方法给出计算p-Henon方程边值问题O(2)对称正解的算法,然后以p-Henon方程中的参数l为分歧参数,在O(2)对称正解解枝上用扩张系统方法求出对称破缺分歧点,进而用解枝转接方法计算出其它具有不同对称性质的正解. An algorithm which was applied to solving the O（2） symmetric positive solutions to the boundary value problem of p-Henon equation was proposed. Taking l in p-Henon equation as a bifurcation parameter, the symmetry-breaking bifurcation point on the branch of the O（2） symmetric positive solutions was found via the extended systems. Finally, other symmetric positive solutions were computed by the branch switching method based on the Liapunov- Schmidt reduction.
作者 李昭祥 杨忠华
机构地区 上海师范大学计算数学系 科学计算上海高校重点实验室
出处 《应用数学和力学》 CSCD 北大核心 2010年第4期481-490,共10页 Applied Mathematics and Mechanics
基金 国家自然科学基金资助项目(10901106) 上海市重点学科建设资助项目(S30405) 上海市自然科学基金资助项目(09ZR1423200) 上海市科委创新资助项目(09YZ150) 上海市教委高校优青培养科研专项基金资助项目(RE948) 上海师范大学科研项目资助(SK200936)
关键词 p-Henon方程 对称破缺分歧 多解 扩张系统 解枝转接 p-Henon equation symmetry-breaking bifurcation multiple solutions extended system branch switching
分类号 O175 [理学—基础数学]
  • 相关文献

参考文献15

  • 1Amann H.Supersolution,monotone iteration and stability[J].J Diff Eq ,1976,21(3):367-377.
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二级参考文献9

  • 1杨忠华,李业忠.求解非线性椭圆型方程边值问题的分歧方法[J].上海师范大学学报（自然科学版）,2005,34(2):17-20. 被引量：5
  • 2Shuang-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
  • 3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
  • 4[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.
  • 5[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.
  • 6[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.
  • 7CHOI Y S,MCKENNA P J.A mountain pass method for the numerical solutions of semi-linear elliptic problems[J].Nonlinear Anal,1993,20:417-437.
  • 8DING 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
  • 9LI Y,ZHOU J X.A minimax method for finding multiple critical points and its application to semi-linear PDEs[J].SIAM J Sci Comput,2002,23:840-865.

共引文献5

同被引文献16

  • 1YANG ZhongHua,LI ZhaoXiang,ZHU HaiLong.Bifurcation method for solving multiple positive solutions to Henon equation[J].Science China Mathematics,2008,51(12):2330-2342. 被引量：6
  • 2Diaz J I. Nonlinear partial differential equations and free boundaries . Vol I, Elliptic equations, Res notes Math 106, Pitman, Boston, 1985.
  • 3Amann H. Supersolution,monotone iteration and stability[J]. J Diff Eq, 1976, 21: 367-377.
  • 4Amann H, Crandall M G. On some existence theorems for semilinear elliptic equations[J]. Indian Univ Math J, 1978, 27: 779-790.
  • 5Chang K C. Infinite dimensional Morse theory and multiple solution problems.Boston:Birkhauser, 1993.
  • 6Struwe M. Variational methods, A series of modern surveys in math. Berlin:Springer-Verlag, 1996.
  • 7Pao C V. Block monotone iterative methods for numerical solutions of nonlinear elliptic equations[J]. Numer Math, 1995, 72: 239-262.
  • 8Deng Y, Chen G, Ni W M, et al. Boundary element monotone iteration scheme for semilinear elliptic partial differential equations[J]. Math Comput, 1996, 65: 943-982.
  • 9Choi Y S , McKenna P J. A mountain pass method for the numerical solutions of semilinear elliptic problems[J]. Nonlinear Anal, 1993, 20: 417-437.
  • 10Ding Z H, Costa D, Chen G. A high-linking algorithm for sign-changing solutions of semilinear elliptic equations[J]. Nonlinear Anal, 1999, 38: 151-172.

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应用数学和力学
2010年 第4期

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