Asymptotic behavior of oscillatory solutions of first order functional delay difference equations

Authors

  • A. Murugesan DEPARTMENT OF MATHEMATICS,GOVERNMENT ARTS COLLEGE (AUTONOMOUS), SALEM - 636 007, TAMIL NADU, INDIA.
  • C. Soundara Rajan DEPARTMENT OF MATHEMATICS, GOVERNMENT ARTS COLLEGE (AUTONOMOUS), SALEM-636007, TAMIL NADU, INDIA.

DOI:

https://doi.org/10.14419/ijamr.v4i2.4234

Published:

2015-03-08

Keywords:

Asymptotic behavior, Delay difference equation, Oscillatory solution.

Abstract

In this paper, we study the asymptotic behavior of oscillatory solutions of the first order functional delay difference equation

\begin{equation*} \quad \quad \quad \quad \quad \quad\quad \quad \quad \Delta x(n)=f(n, x(n-\tau)),\quad n\geq n_0. \quad \quad \quad \quad \quad \quad \quad \quad \quad\quad \quad \quad \quad \quad \quad\quad \quad \quad\quad \quad (*)\end{equation*}

A new sufficient condition is established under which every oscillatory solution of (*) tends to zero asymptotically.

Author Biography

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

ASSISTANT PROFESSOR, DEPARTMENT OF MATHEMATICS

References

[1] R. P. Agarwal, Advanced Topics in Difference Equations, Kluwer Academic Publishers Inc., 1997.

[2] R. P. Agarwal, Difference Equations and Inequalities: Theory, Methods, and Applications, Marcel Dekker, Inc., New York, 1999.

[3] M. P. Chen and B. Liu, Asymptotic behavior of solutions of first order nonlinear delay difference equations, Comput. Math. Appl., 32(1996), 9-13.

[4] L. H. Erbe, H. Xian and J. S. Yu, Global stability of a linear nonautonomous delay difference equation, J. Difference Equ. Appl., 1(1995), 151-161.

[5] I. Gyri and G. Ladas, Oscillation Theory of Delay Differential Equations with Applications, Oxford University Press, Oxford, (1991).

[6] G. Ladas, Explicit conditions for the oscillation of difference equations, Math. Anal. Appl., 153(1990), 276-287.

[7] B. S. Lalli, Oscillation theorems for neutral difference equations, Comput. Math. Appl., 28(1994), 191-202.

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

[9] R. E. Mickens, Difference Equations, Van Nostrand Reinhold Company Inc., New York 1987.

[10] Ch. G. Philos, On oscillations of some difference equations, Funkcialaj Ekvacioj, 34(1991), 157-172.

[11] X. H. Tang and J. S. Yu, A further result on the oscillation of delay difference equations, Comput. Math. Appl., 38(1999), 229-237.

[12] J. S. Yu, Asymptotic stability for a linear difference equation with variable delay, Comput. Math. Appl., 36(1998), 202-210.

[13] Z. Zhou, J. S. Yu and Z. C. Wang, Global attractivity of neutral difference equations, Comput. Math. Appl., 36(6)(1998), 1-10.

View Full Article: