Existence Results for Nonoscillatory Solutions of Third Order Nonlinear Neutral Difference Equations - Thandapani, E.; Karunakaran, R.; Arockiasamy, I. M. (Sarajevo Journal of Mathematics, 2024)
In this paper the authors consider the third order neutral difference equation \begin{equation*} Δ ^{3}\left( x_{n}+p_{n}x_{n-k}\right) +q_{n}f\left( x_{n-\ell }\right) =h_{n} \end{equation*} where $\left\{ p_{n}\right\} ,\left\{ q_{n}\right\} ,\left\{ h_{n}\right\} \ $are real sequences. They use Krasnoselskii's fixed point theorem to establish the existence of nonoscillatory solutions. The results are illustrated with examples. 2000 Mathematics Subject Classification. 39A10