奇异Sturm-Liouville边值问题的谱理论  

Spectral Theory of Singular Sturm-Liouville Boundary Value Problem

作　　者：孟宪瑞[1] 曹有好 佟玉霞[1] 

机构地区：[1]河北联合大学数学系,河北唐山063009 [2]中油国际(土库曼斯坦)勘探开发公司,北京100101

出　　处：《郑州大学学报（理学版）》2013年第1期34-37,共4页Journal of Zhengzhou University:Natural Science Edition

基　　金：河北省自然科学基金资助项目;编号A2010000910

摘　　要：研究了带奇异项的Sturm-Liouville边值问题的谱定理.将所研究的问题转换成等价的积分方程,通过积分方程定义算子,利用Arzela定理及Green函数的对称性得到此算子是线性自共轭全连续算子,由线性自共轭全连续算子的性质得到原边值问题的谱理论.The spectral theory of singular Sturm-Liouville boundary value problem was investigated.An integral equation equivalent to the boundary value problem was constructed.Via this integral equation,an operator was defined,which was proved to be a linear self-adjoint completely continuous differential operator by Arzela theorem and the symmetry of Green function.By properties of linear self-adjoint completely continuous operators,the spectral theory of the singular Sturm-Liouville boundary value problem was obtained.

关 键 词：谱 全连续 算子 

分 类 号：O175.8[理学—数学]