Oscillatory behavior for nonlinear homogeneous neutral difference equations of second order with coefficient changing sign - Ajit Kumar Bhuyan; Laxmi Narayan Padhy; Radhanath Rath (Electronic Journal of Differential Equations, 2020)
In this article, we obtain sufficient conditions so that all solutions of the neutral difference equation $$ Δ^{2}\big(y_n-p_n L(y_{n-s})\big) + q_nG(y_{n-k})=0, $$ and all unbounded solutions of the neutral difference equation $$ Δ^{2}\big(y_n-p_n L(y_{n-s})\big) + q_nG(y_{n-k}) -u_nH(y_{α(n)})=0 $$ are oscillatory, where $Δ y_n = y_{n+1}-y_n$, $Δ^2 y_n =Δ(Δ y_n)$. Different types of super linear and sub linear conditions are imposed on $G$ to prevent the solution approaching zero or $± ∞$.