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Oscillation of Higher-Order of System of Difference Equations with Continuous Arguments

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Author(s): Özkan Öcalan | Umut Mutlu Özkan

Journal: Selçuk Journal of Applied Mathematics
ISSN 1302-7980

Volume: 9;
Issue: 1;
Start page: 23;
Date: 2008;
Original page

Keywords: Oscillation | difference equations | characteristic equation | logarithmic norm.

ABSTRACT
This paper is concerned with the oscillatory behavior of all solutions of the higher-order of system of difference equations with continuous arguments∇_{τ}ⁿy(t)+∑_{i=1}^{m}P_{i}y(t-σ_{i})=0where P_{i}∈ℝ^{s×s} and τ,σ_{i}∈ℝ for i=1,2,…,m, and ∇_{τ} is a backward difference operator, defined by ∇_{τ}y(t) =y(t)-y(t-τ).