張志凱

（1．內(nèi)蒙古工業(yè)大學(xué) 理學(xué)院,內(nèi)蒙古 呼和浩特 010051;2．肇慶學(xué)院 計(jì)算機(jī)學(xué)院,廣東 肇慶 526061)

具有間斷點(diǎn)的Sturm-Liouville問(wèn)題的自伴邊界條件

張志凱1,2

（1．內(nèi)蒙古工業(yè)大學(xué) 理學(xué)院,內(nèi)蒙古 呼和浩特 010051;2．肇慶學(xué)院 計(jì)算機(jī)學(xué)院,廣東 肇慶 526061)

在研究二階Sturm-Liouville問(wèn)題的邊界條件時(shí)，通常會(huì)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(lèi)型．在研究具有間斷點(diǎn)的Sturm-Liouville問(wèn)題的自伴邊界條件時(shí)，可考慮將其分為2種情況:在間斷點(diǎn)處有轉(zhuǎn)化條件和在間斷點(diǎn)處沒(méi)有轉(zhuǎn)化條件時(shí)自伴邊界條件的分類(lèi)．

Sturm-Liouville問(wèn)題；自伴邊界條件；間斷點(diǎn)

1 預(yù)備知識(shí)

本文在導(dǎo)師王忠教授的悉心指導(dǎo)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(zé)任編輯：陳 靜）

2010－12－20

廣東省自然科學(xué)基金資助項(xiàng)目(9251064101000015)

張志凱(1985－),男,山東濰坊人,內(nèi)蒙古工業(yè)大學(xué)與肇慶學(xué)院聯(lián)合培養(yǎng)碩士研究生．