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.
    2015-03-08
    https://doi.org/10.14419/ijamr.v4i2.4234
  • Asymptotic behavior, Delay difference equation, Oscillatory solution.

  • 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. [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.

  • Downloads

  • How to Cite

    Murugesan, A., & Soundara Rajan, C. (2015). Asymptotic behavior of oscillatory solutions of first order functional delay difference equations. International Journal of Applied Mathematical Research, 4(2), 234-244. https://doi.org/10.14419/ijamr.v4i2.4234