Bounded solutions and asymptotic stability of nonlinear second-order neutral difference equations with quasi-differences

Authors : Magdalena Nockowska ROSIAK

Pages : 1956-1969

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Publication Date : 0000-00-00

Article Type : Research Paper

Abstract :This work is devoted to the study of the nonlinear second-order neutral difference equations with quasi-differences of the form $$ \Delta \leftinsert ignore into journalissuearticles values( r_{n} \Delta \leftinsert ignore into journalissuearticles values( x_{n}+q_{n}x_{n-\tau}\right);\right);= a_{n}finsert ignore into journalissuearticles values(x_{n-\sigma});+b_n $$ with respect to $insert ignore into journalissuearticles values(q_n);$. For $q_n\to1$, $q_n\ininsert ignore into journalissuearticles values(0,1);$ 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|
Keywords : Nonlinear neutral difference equation, Krasnoselskii`s fixed point theorem, approximation