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Applied Mathematics and Mechanics (English Edition) ›› 2010, Vol. 31 ›› Issue (4): 511-520.doi: https://doi.org/10.1007/s10483-010-0411-6

• Articles • 上一篇    下一篇

Bifurcation method for solving multiple positive solutions to boundary value problem of p-Henon equation on the unit disk

李昭祥 杨忠华   

  1. Department of Mathematics, Scientific Computing Key Laboratory of Shanghai University, Shanghai Normal University, Shanghai 200234, P. R. China
  • 收稿日期:2009-05-27 修回日期:2010-01-31 出版日期:2010-04-20 发布日期:2010-04-01

Bifurcation method for solving multiple positive solutions to boundary value problem of p-Henon equation on the unit disk

 LI Zhao-Xiang, YANG Zhong-Hua   

  1. Department of Mathematics, Scientific Computing Key Laboratory of Shanghai University, Shanghai Normal University, Shanghai 200234, P. R. China
  • Received:2009-05-27 Revised:2010-01-31 Online:2010-04-20 Published:2010-04-01

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被引次数

20

摘要： In this paper, an algorithm is proposed to solve the O(2) symmetric positive solutions to the boundary value problem of the p-Henon equation. Taking l in the p-Henon equation as a bifurcation parameter, the symmetry-breaking bifurcation point on the branch of the O(2) symmetric positive solutions is found via the extended systems. The other symmetric positive solutions are computed by the branch switching method based on the Liapunov-Schmidt reduction.

Abstract: In this paper, an algorithm is proposed to solve the O(2) symmetric positive solutions to the boundary value problem of the p-Henon equation. Taking l in the p-Henon equation as a bifurcation parameter, the symmetry-breaking bifurcation point on the branch of the O(2) symmetric positive solutions is found via the extended systems. The other symmetric positive solutions are computed by the branch switching method based on the Liapunov-Schmidt reduction.

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