言語
英語
著者
内容記述(抄録等)
This paper deals with nonoscillation problem about the non-autonomous linear difference system
xn = Anxn−1, n = 1,2,...,
where An is a 2×2 variable matrix that is nonsingular for n ∈ N. In the special case that A is a constant matrix, it is well-known that all non-trivial solutions are nonoscillatory if and only if all eigenvalues of A are positive real numbers; namely, detA > 0, trA > 0 and detA/(trA) 2 ≤ 1/4. The well-known result can be said to be an analogy of ordinary differential equations. The results obtained in this paper extend this analogy result. In other words, this paper clarifies the distinction between difference equations and ordinary differential equations. Our results are explained with some specific examples. In addition, figures are attached to facilitate understanding of those examples.
主題
Linear difference equations
Non-autonomous
Nonoscillation
Riccati transformation
Sturm’s separation theorem
掲載誌名
Linear Algebra and its Applications
531
開始ページ
22
終了ページ
37
ISSN
0024-3795
発行日
2017-10-15
DOI
資料タイプ
学術雑誌論文
ファイル形式
PDF
著者版/出版社版
著者版
部局
総合理工学部 数理科学科