Electron. J. Differential Equations, Vol. 2020 (2020), No. 87, pp. 1-14.

Oscillatory behavior for nonlinear homogeneous neutral difference equations of second order with coefficient changing sign

Ajit Kumar Bhuyan, Laxmi Narayan Padhy, Radhanath Rath

In this article, we obtain sufficient conditions so that all solutions of the neutral difference equation

and all unbounded solutions of the neutral difference equation

are oscillatory, where $\Delta y_n = y_{n+1}-y_n$, $\Delta^2 y_n =\Delta(\Delta y_n)$. Different types of super linear and sub linear conditions are imposed on G to prevent the solution approaching zero or $\pm \infty$.

Submitted June 3, 2020. Published August 12, 2020.
Math Subject Classifications: 39A10, 39A12.
Key Words: Oscillatory solution; nonoscillatory solution; asymptotic behavior; difference equation.

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Ajit Kumar Bhuyan
Dept. Of Mathematics
Sai international School
Bhubaneswar, Odisha, India
email: ajitbhuyan13@gmail.com
Laxmi Narayan Padhy
Dept. of Math and Computer Science
Konark Institute of Science and Technology
Bhubaneswar, Odisha, India
email: padhyln@gmail.com
Radhanath Rath
VSSUT Burla, 768018
Retired Principalhallikote Autonomous College
Berhampur, Odisha, India
email: radhanathmath@yahoo.co.in

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