复系数奇异Sturm-Liouville方程的极限点和极限圆分类

数学物理学报 ›› 2010, Vol. 30 ›› Issue (6): 1534-1541.

复系数奇异Sturm-Liouville方程的极限点和极限圆分类

景海斌¹|綦建刚²|岳崇山³

1.河北建筑工程学院数理系河北张家口 075024|2.山东大学威海分校数学与统计学院山东威海 264209; 3.河北北方学院数学系河北张家口 075000

收稿日期:2008-12-17 修回日期:2010-01-06 出版日期:2010-12-25 发布日期:2010-12-25
基金资助:
山东省自然科学基金(Y2008A02)资助

Limit-point and Limit-circle Classification of |Singular Sturm-Liouville Equations with Complex Coefficients

JING Hai-Bin¹, QI Jian-Gang², YUE Chong-Shan³

1.Department of Mathematics and Physics, Hebei Institute of Architecture and Civil Engineering, Hebei Zhangjiakou 075000;
2.Faculty of Mathematics and Statistics, Shandong University at Weihai, Shandong Weihai 264209;
3.Department of Mathematics, Hebei North University, Hebei Zhangjiakou 075000

Received:2008-12-17 Revised:2010-01-06 Online:2010-12-25 Published:2010-12-25
Supported by:
山东省自然科学基金(Y2008A02)资助

摘要/Abstract

摘要：

该文利用对称Hamilton微分系统的极限点、极限圆分类理论(不同于B.M.Brown等人采用的方法), 给出了复系数奇异Sturm-Liouville方程的Sims分类:极限点1型、极限点2型和极限圆型; 并且建立了极限点1型的两个判别准则; 最后通过举例肯定地回答了B.M.Brown等人提出的开问题.

关键词: 奇异Sturm-Liouville方程, 极限点型, 复系数

Abstract:

By using limit-point(circle) classification theory of symmetric Hamiltonian differential systems, different from the method used by B.M.Brown et al, the paper gives the Sims classification of singular Sturm-Liouville equations with complex coefficients: limit-point-1 case, limit-point-2 case and limit-circle case. Then two limit-point-1 case criteria are obtained. Furthermore, the authors give an affirmative answer to the open problem of B.M.Brown et al by an example.

Key words: Singular Sturm-Liouville equations, Limit-point case, Complex coefficients

中图分类号:

34B24

景海斌, 綦建刚, 岳崇山. 复系数奇异Sturm-Liouville方程的极限点和极限圆分类[J]. 数学物理学报, 2010, 30(6): 1534-1541.

JING Hai-Bin, QI Jian-Gang, YUE Chong-Shan. Limit-point and Limit-circle Classification of |Singular Sturm-Liouville Equations with Complex Coefficients[J]. Acta mathematica scientia,Series A, 2010, 30(6): 1534-1541.

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[2]	杨杰, 綦建刚, 景海斌. 奇异哈密顿微分系统的粘结引理和亏指数[J]. 数学物理学报, 2011, 31(3): 652-661.