Oscillation condition for second order half-linear advanced difference equation with variable coefficients
Authors :
A. Murugesan 1* and C. Jayakumar 2
Author Address :
1 Department of Mathematics, Government Arts College (Autonomous), Salem-636007, Tamil Nadu, India.
2 Department of Mathematics, Mahendra Arts & Science College, Kalipatti-637501, Tamil Nadu, India.
*Corresponding author.
Abstract :
Our aim of this paper is to determine sufficient condition for the oscillation of all solutions of second order half-linear difference equations with variable co-efficients of advanced argument of the form $ \Delta\left[r(n)\left(\Delta y(n)\right)^\alpha\right] + q(n) y^\alpha(n+\sigma)=0$, $n\geq n_0 $, where $\Delta$ is the forward difference operator given by $\Delta x(n)=x(n+1)-x(n)$, when $\sum_{n =n_0}^\infty \frac{1}{r^\frac{1}{\alpha}(s)} < \infty$. Our results improve and simplify a number of existing ones.
Keywords :
Oscillation, second order, half-linear, advanced difference equations.
DOI :
Article Info :
Received : August 14, 2020; Accepted : October 24, 2020.
