计算圆域上p-Henon方程边值问题多个正解的分歧方法  

Bifurcation Method for Solving Multiple Positive Solutions to Boundary Value Problem of p-Henon Equation on the Unit Disk

作　　者：李昭祥[1,2] 杨忠华[1,2] 

机构地区：[1]上海师范大学计算数学系,上海200234 [2]科学计算上海高校重点实验室,上海200234

出　　处：《应用数学和力学》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)

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.

关 键 词：p-Henon方程 对称破缺分歧 多解 扩张系统 解枝转接 

分 类 号：O175[理学—数学]