非局部奇异二阶微分方程的Weyl分类  

Weyl Classification of Nonlocal Singular Second Order Differential Equations

作　　者：刘志文 綦建刚 徐亚飞 Liu Zhiwen;Qi Jiangang;Xu Yafei(College of Mathematics and Statistics,Shandong University at Weihai,Shandong Weihai 264209)

机构地区：[1]山东大学(威海)数学与统计学院,山东威海264209

出　　处：《数学物理学报（A辑）》2020年第5期1295-1304,共10页Acta Mathematica Scientia

基　　金：国家自然科学基金(11771253)。

摘　　要：该文考虑一类带有非局部项的二阶奇异Sturm-Liouville方程.给出了此类方程极限点(圆)型的定义和这两类划分的充分必要条件.此外,该文也研究了上述方程在实轴上平方可积解的个数,并建立了相应的充分必要条件.结果表明非局部问题的情形与经典局部问题之间有本质区别.The present paper is concerned with the Weyl classification of second order singular Sturm-Liouville equations with nonlocal point potential.We give the Weyl classification for these equations and give sufficient and necessary conditions for the division of these two kinds.Furthermore,the most important part is the situation of square integrable solutions forλon the real axis,which has essential differences with the classical equation,and corresponding sufficient and necessary conditions are also obtained.

关 键 词：极限点(圆) 非局部势 奇异Sturm-Liouville方程 平方可积解 

分 类 号：O175[理学—数学]