Turkish Journal of Mathematics
Abstract
This work is devoted to the study of the nonlinear second-order neutral difference equations with quasi-differences of the form $$ \Delta \left( r_{n} \Delta \left( x_{n}+q_{n}x_{n-\tau}\right)\right)= a_{n}f(x_{n-\sigma})+b_n $$ with respect to $(q_n)$. For $q_n\to1$, $q_n\in(0,1)$ the standard fixed point approach is insufficient to get the existence of the bounded solution, so we combine this method with an approximation technique to achieve our goal. Moreover, for $p\ge 1$ and $\sup q_n
DOI
10.3906/mat-1708-29
Keywords
Nonlinear neutral difference equation, Krasnoselskii's fixed point theorem, approximation
First Page
1956
Last Page
1969
Recommended Citation
ROSIAK, M. N (2018). Bounded solutions and asymptotic stability of nonlinear second-order neutral difference equations with quasi-differences. Turkish Journal of Mathematics 42 (4): 1956-1969. https://doi.org/10.3906/mat-1708-29
