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

Abstract:
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.
DOI: 10.58997/ejde.2020.87

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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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