Necessary and sufficient conditions for oscillation of first order neutral delay difference equations

  • Authors

    • A. Murgesan DEPARTMENT OF MATHEMATICS,GOVERNMENT ARTS COLLEGE (AUTONOMOUS), SALEM - 636 007, TAMIL NADU, INDIA.
    • P. Sowmiya DEPARTMENT OF MATHEMATICS, GOVERNMENT ARTS COLLGE (AUTONOMOUS), SALEM - 636 007, TAMIL NADU, INDIA.
    2015-04-25
    https://doi.org/10.14419/gjma.v3i2.4560
  • Oscillatory behavior, Neutral, Delay difference equation, Constant coefficients.
  • Abstract

    In this paper, we obtained some necessary and sufficient conditions for oscillation of all the solutions of the first order neutral delay difference equation with constant coefficients of the form
    \begin{equation*} \quad \quad \quad \quad \Delta[x(n)-px(n-\tau)]+qx(n-\sigma)=0, \quad \quad n\geq n_0 \quad \quad \quad \quad \quad \quad {(*)} \end{equation*}
    by constructing several suitable auxiliary functions. Some examples are also given to illustrate our results.

    Author Biography

    • A. Murgesan, DEPARTMENT OF MATHEMATICS,GOVERNMENT ARTS COLLEGE (AUTONOMOUS), SALEM - 636 007, TAMIL NADU, INDIA.
      ASSISTANT PROFESSOR, DEPARTMENT OF MATHEMATICS
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  • How to Cite

    Murgesan, A., & Sowmiya, P. (2015). Necessary and sufficient conditions for oscillation of first order neutral delay difference equations. Global Journal of Mathematical Analysis, 3(2), 61-72. https://doi.org/10.14419/gjma.v3i2.4560

    Received date: 2015-03-29

    Accepted date: 2015-04-20

    Published date: 2015-04-25