【作者】 朱海龙；

【导师】 杨忠华；

【作者基本信息】 上海师范大学 ， 计算数学， 2007， 硕士

【摘要】 本文讨论平面单位圆上Henon方程的齐次Dirichlet边界条件的边值问题的多解计算,这里Ω为单位圆,（?）Ω是Ω的边界,r = （x² + y²）^1/2,l≥0,p≥1/2在天体物理中称为多方指数.本文运用Liapunov-Schmidt约化和对称破缺分歧理论求解和计算了上述问题的带不同对称性的解,特别是带有不同对称性的正解.分歧方法的优点是它能计算出尽可能多的带有不同对称性的解,并且根据对称性能有效地降低计算工作量.更多还原

【Abstract】 In this dissertation, we compute and visualize multiple solutions of the boundary valueproblem of the Henon equation on the disk of planewhereΩis a unit circle, （?）Ωis the boundary ofΩ, r = （x² + y²）^1/2,l≥0,p≥1/2 which is calledpolytropic exponent in astrophysics.Using the Liapunov-Schimdt method and symmetry-breaking bifurcation theory, we computedifferent symmetry solutions of problem（0-1）, especially the positive solutions with different sym-metry.The bifurcation method has two kind of advantage. Firstly, it can be used to compute the so-lutions with different symmetry as many as possible; Secondly, it can simplify the computationdue to the symmetry.更多还原