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.

DOI:

https://doi.org/10.14419/gjma.v3i2.4560

Published:

2015-04-25

Keywords:

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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