Electron. J. Diff. Eqns., Vol. 2009(2009), No. 29, pp. 1-11.

Oscillation criteria for first-order systems of linear difference equations

Arun Kumar Tripathy

Abstract:
In this article, we obtain conditions for the oscillation of vector solutions to the first-order systems of linear difference equations
$$\displaylines{ x(n+1)=a(n)x+b(n)y \cr y(n+1)=c(n)x+d(n)y }$$
and
$$\displaylines{ x(n+1)=a(n)x+b(n)y+f_1(n) \cr y(n+1)=c(n)x+d(n)y+f_2(n) }$$
where $a(n), b(n), c(n), d(n) $ and $f_i(n), i=1, 2$ are real valued functions defined for $n \geq 0$.

Submitted November 29, 2008. Published February 9, 2009.
Math Subject Classifications: 39A10, 39A12.
Key Words: Oscillation; linear system; difference equation.

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Arun Kumar Tripathy
Department of Mathematics
Kakatiya Institute of Technology and Science
Warangal-506015, India
email: arun_tripathy70@rediffmail.com

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