Asymptotic behavior of first order delay difference equation with a forcing term

Authors

  • A. Murugesan DEPARTMENT OF MATHEMATICS,GOVERNMENT ARTS COLLEGE (AUTONOMOUS), SALEM - 636 007, TAMIL NADU, INDIA.
  • K. Venkataramanan DEPARTMENT OF MATHEMATICS, VYSYA COLLEGE, SALEM-63603, TAMIL NADU, INDIA.

DOI:

https://doi.org/10.14419/ijamr.v4i2.4244

Published:

2015-03-08

Keywords:

Asymptotic Behavior, Delay Difference Equation, Oscillatory Solution.

Abstract

In this paper, we study the asymptotic behavior of solutions of the following first order forced delay difference equation \begin{equation*}\quad \quad \quad \quad \Delta x(n)+p(n)f(x(n-\tau))+r(n)=0,\quad n\geq 0. \quad \quad \quad \quad  (*)\end{equation*} Some sufficient conditions for every solution of (*) to tend to zero are established.

Author Biography

A. Murugesan, DEPARTMENT OF MATHEMATICS,GOVERNMENT ARTS COLLEGE (AUTONOMOUS), SALEM - 636 007, TAMIL NADU, INDIA.

ASSISTANT PROFESSOR, DEPARTMENT OF MATHEMATICS

References

[1] S. S. Chang, G. Zhang and S. T. Li, Stability of oscillatory solutions of difference equations with delay, Taiwanese J. of Math, 3(4) (1999), 503-515.

[2] J. R. Graef and C. Qian, Asymptotic behavior of a forced difference equation, J. Math. Anal. Appl., 203(1996), 388-400.

[3] I. Katsunori, Asymptotic analysis for linear difference equations, Trans. Amer. Math. Soc., 349(1997), 4107-4142.

[4] V. L. J. Kocic and G. Ladas, Global behavior of nonlinear difference equations of higher order with applications, Kluwer Academic, 1993.

[5] G. Ladas and Y. G. Sfices, Asymptotic behavior of oscillatory solutions, Hiroshima Math. J., 18(1988), 351-359.

[6] G. Ladas, C. Qian, P. N. Vlahos and J. Y. Yan, Stability of solution of linear nonautonomous difference equations , Appl. Anal., 4(1) (1991), 183-191.

[7] N. Parhi, Behavior of solutions of delay-difference equations of first order, Indian J. Pure Appl. Math., 33(1) (2002), 31-43.

[8] Yuji Liu and Weigao Ge, Global asymptotic behavior of solutions of a forced delay difference equation, Comput. Math. Appl., 47(2004), 1211-1224.

View Full Article: