On classification of second-order differential equations with complex coefficients

被引：15

作者：

Sun, Huaqing ^{[1
]}

Qi, Jiangang ^{[1
]}

机构：

[1] Shandong Univ Weihai, Dept Math, Weihai 264209, Shandong, Peoples R China

来源：

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS | 2010年 / 372卷 / 02期

关键词：

Sturm-Liouville differential equation; Non-self-adjoint; Hamiltonian system; Limit point case; Limit circle case; LIMIT-POINT CRITERION; HAMILTONIAN-SYSTEMS; SPECTRAL EXACTNESS; INCLUSION; OPERATORS;

D O I：

10.1016/j.jmaa.2010.07.051

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

This paper is concerned with the deficiency index problem of second-order differential equations with complex coefficients. It is known that this class of equations is classified into cases I, II, and III according to the number of linearly independent solutions in suitable weighted square integrable spaces. In this study, the original equation is reformulated into a new formally self-adjoint differential system by introducing a new spectral parameter and the relationship between the classifications of the equation and the system is obtained. Moreover, the exact dependence of cases II and III on the corresponding half planes is given and some criteria of the three cases are established. (C) 2010 Elsevier Inc. All rights reserved.

引用

页码：585 / 597

页数：13

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