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On classification of singular matrix difference equations of mixed order

Part of: Boundary value problems

Published online by Cambridge University Press:  11 August 2023

Li Zhu ,
Huaqing Sun  and
Bing Xie
Li Zhu
Affiliation:
College of Sciences, Northeastern University, Shenyang, Liaoning 110819, P. R. China (zhulimathematics@163.com) Department of Mathematics, Shandong University at Weihai, Weihai, Shandong 264209, P. R. China
Huaqing Sun*
Affiliation:
College of Sciences, Northeastern University, Shenyang, Liaoning 110819, P. R. China (sunhuaqing@mail.neu.edu.cn)
Bing Xie
Affiliation:
Department of Mathematics, Shandong University at Weihai, Weihai, Shandong 264209, P. R. China (xiebing@sdu.edu.cn)
*
*Corresponding author.
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Abstract

This paper is concerned with singular matrix difference equations of mixed order. The existence and uniqueness of initial value problems for these equations are derived, and then the classification of them is obtained with a similar classical Weyl's method by selecting a suitable quasi-difference. An equivalent characterization of this classification is given in terms of the number of linearly independent square summable solutions of the equation. The influence of off-diagonal coefficients on the classification is illustrated by two examples. In particular, two limit point criteria are established in terms of coefficients of the equation.

Keywords

block operator matrixmatrix differential equationmatrix difference equationlimit point caselimit circle case

MSC classification

Primary: 34B20: Weyl theory and its generalizations

Information

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 154 , Issue 4 , August 2024 , pp. 1235 - 1258
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Copyright
Copyright © The Author(s), 2023. Published by Cambridge University Press on behalf of The Royal Society of Edinburgh

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