Classification of Non-symmetric Sturm-Liouville Systems and Operator Realizations

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• 作者：Bing Xie (1)
  Xinwei Guo (1)
  Jiangang Qi (1)
  
• 关键词：Sturm ; Liouville differential system ; Non ; self ; adjoint ; Hamiltonian system ; Limit point (circle) case ; J ; Self ; adjoint extension ; 34B20 ; 34B24
• 刊名：Acta Applicandae Mathematicae
• 出版年：2013
• 出版时间：June 2013
• 年：2013
• 卷：125
• 期：1
• 页码：27-47
• 全文大小：756KB
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• 作者单位：Bing Xie (1)
  Xinwei Guo (1)
  Jiangang Qi (1)
  
  1. Department of Mathematics, Shandong University (Weihai), Weihai, 264209, P.R. China
  
• ISSN：1572-9036

文摘

The main objective of this paper is to give a classification of Sturm-Liouville differential equations with non-symmetric matrices coefficients in terms of the number of square integrable solutions of the system and its conjugate system. The conjugate system is innovatively introduced to get the classification. Furthermore, the asymptotic behavior of elements in the maximal domain is studied. As applications, the J-self-adjoint operator realizations are given for a special case in the classification.