具有間斷點的Sturm-Liouville問題的自伴邊界條件

張志凱

（1．內蒙古工業大學 理學院,內蒙古 呼和浩特 010051;2．肇慶學院 計算機學院,廣東 肇慶 526061)

具有間斷點的Sturm-Liouville問題的自伴邊界條件

張志凱1,2

（1．內蒙古工業大學 理學院,內蒙古 呼和浩特 010051;2．肇慶學院 計算機學院,廣東 肇慶 526061)

在研究二階Sturm-Liouville問題的邊界條件時，通常會將這些邊界條件分為分離型、耦合型及特殊的退化型3種類型．在研究具有間斷點的Sturm-Liouville問題的自伴邊界條件時，可考慮將其分為2種情況:在間斷點處有轉化條件和在間斷點處沒有轉化條件時自伴邊界條件的分類．

Sturm-Liouville問題；自伴邊界條件；間斷點

1 預備知識

本文在導師王忠教授的悉心指導下完成，筆者在此深表謝意！

[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

（責任編輯：陳 靜）

2010－12－20

廣東省自然科學基金資助項目(9251064101000015)

張志凱(1985－),男,山東濰坊人,內蒙古工業大學與肇慶學院聯合培養碩士研究生．