Magdalena NOCKOWSKA-ROSIAK

6797

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

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|
Keywords:

Nonlinear neutral difference equation, Krasnoselskii's fixed point theorem approximation,

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Turkish Journal of Mathematics-Cover
  • ISSN: 1300-0098
  • Yayın Aralığı: 6
  • Yayıncı: TÜBİTAK
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