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eng
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Description
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.
Subject
Linear difference equations
Non-autonomous
Nonoscillation
Riccati transformation
Sturm’s separation theorem
Journal Title
Linear Algebra and its Applications0
Volume
531
Start Page
22
End Page
37
ISSN
0024-3795
Published Date
2017-10-15
DOI
NII Type
Journal Article
Format
PDF
Text Version
著者版
OAI-PMH Set
Faculty of Science and Engineering
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