半线性多调和方程解的分支

数学物理学报 ›› 2010, Vol. 30 ›› Issue (1): 227-238.

半线性多调和方程解的分支

金玲玉, 王霞, 房少梅

华南农业大学理学院广州 510642

收稿日期:2008-05-26 修回日期:2009-09-20 出版日期:2010-01-01 发布日期:2010-01-01
基金资助:
国家自然科学基金(10871075)、广东省自然科学基金(05300889)、广东省教育厅项目(4900-209031)和华南农业大学校长基金(4900-K07418)资助.

Branches of |Solutions to Semilinear Polyharmonic Equations

JIN Ling-Yu, WANG Xia, FANG Shao-Mei

College of Science, South China Agriculture University, |Guangzhou 510642

Received:2008-05-26 Revised:2009-09-20 Online:2010-01-01 Published:2010-01-01
Supported by:
国家自然科学基金(10871075)、广东省自然科学基金(05300889)、广东省教育厅项目(4900-209031)和华南农业大学校长基金(4900-K07418)资助.

摘要/Abstract

摘要：

该文主要讨论一类多调和方程, 通过研究此方程对应的线性化问题本征谱,得到了方程的全局分支结果. 所讨论的方法主要依赖于P. M. Fitzpatrick, J. Pejsachowicz 和 P. J. Rabier^[12] C² Fredholm算子的度理论思想.

关键词: 分支, 多调和方程, 度理论

Abstract:

This paper considers a class of nonlinear polyharmonic eigenvalue problem, describes the behavior of the branches of solutions emanating from an eigenvalue of odd multiplicity below the essential spectrum of the linearized problem. The discussion is based on the degree theory for C² proper Fredholm maps developed by P. M. Fitzpatrick, J. Pejsachowicz and P. J. Rabier^[7].

中图分类号:

35J65

金玲玉, 王霞, 房少梅. 半线性多调和方程解的分支[J]. 数学物理学报, 2010, 30(1): 227-238.

JIN Ling-Yu, WANG Xia, FANG Shao-Mei. Branches of |Solutions to Semilinear Polyharmonic Equations[J]. Acta mathematica scientia,Series A, 2010, 30(1): 227-238.

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