具有间断点的Sturm-Liouville问题的自伴边界条件

张志凯

（1．内蒙古工业大学 理学院,内蒙古 呼和浩特 010051;2．肇庆学院 计算机学院,广东 肇庆 526061)

具有间断点的Sturm-Liouville问题的自伴边界条件

张志凯1,2

（1．内蒙古工业大学 理学院,内蒙古 呼和浩特 010051;2．肇庆学院 计算机学院,广东 肇庆 526061)

在研究二阶Sturm-Liouville问题的边界条件时，通常会将这些边界条件分为分离型、耦合型及特殊的退化型3种类型．在研究具有间断点的Sturm-Liouville问题的自伴边界条件时，可考虑将其分为2种情况:在间断点处有转化条件和在间断点处没有转化条件时自伴边界条件的分类．

Sturm-Liouville问题；自伴边界条件；间断点

1 预备知识

本文在导师王忠教授的悉心指导下完成，笔者在此深表谢意！

[1] KONG Q,WU H,ZETTL A.Geometric aspects of Sturm-Liouville problems I.Structures on spaces of boundary conditions[J].Proceedings of the Royal Society of Edinburgh,2000,130A:561-589.

[2] CAO Xifang,WANG Zhong,WU Hongyou.On the boundary conditions in self-adjoint multi-interval Sturm-Liouville problems[J].Linear Algebra and its Applications,2009,430(11/12):2 877-2 889.

[3] ALTINISIK N,KADAKAL M,MUKHTAROV O S.Eignvalues and eignfunctions of discontinuous Sturm-Liouville problems with eigenparameter-dependent boundary conditions[J].Acta Mathematica Hunger,2004,102(1/2):159-175.

Self-adjoint Boundary of Sturm-Liouville Problem Conditions with a Discontinuous Point

ZHANG Zhikai1,2

(1.College of Science,Inner Mongolia University of Technology,Hohhot,Inner Mongolia 010051,China;2.School of Computer Science,Zhaoqing University,Zhaoqing,Guangdong 526061,China)

In the study of second order Sturm-Liouville problems,these boundary conditions are generally divided into separated type and the coupled type as well as the special degradation type.In the study of discontinuous point Sturm-Liouville problems with self-adjoint boundary conditions,it's classified into two kinds,namely converting conditions in discontinuous points,and no converting conditions from self-adjoint boundary in discontinuous points.

Sturm-Liouville problem;self-adjoint boundary conditions;discontinuous points

O175．3

A

1009－8445（2011）02－0001－07

（责任编辑：陈 静）

2010－12－20

广东省自然科学基金资助项目(9251064101000015)

张志凯(1985－),男,山东潍坊人,内蒙古工业大学与肇庆学院联合培养硕士研究生．