Oscillation of second order nonlinear difference equations with super-linear neutral term

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Authors :

Govindasamy Ayyappan 1 * and Gunasekaran Nithyakala 2

Author Address :

1 Department of Mathematics, Periyar University College of Arts and Science, Pappireddipatti -636905, Tamilnadu, India.
2 Department of Mathematics, Periyar University, Salem-636011, Tamilnadu, India.

*Corresponding author.

Abstract :

In this paper, the authors establish some new conditions for the oscillation of second order nonlinear difference equation of the form $$Deltaleft(a_n Delta left(y_n+p_n y_{n-k}^alpha ight) ight)+q_n y_{n+1-ell}^eta=0,$$ where $alpha>1$ and $eta$ are ratio of odd positive integers. Examples are provided to illustrate the importance of the main results.

Keywords :

Superlinear neutral term, nonlinear difference equation, oscillation.



Article Info :

Received : April 06, 2019; Accepted : May 29, 2019.



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