Opuscula Math. 39, no. 1 (2019), 61-75
https://doi.org/10.7494/OpMath.2019.39.1.61

Opuscula Mathematica

# On the convergence of solutions to second-order neutral difference equations

Małgorzata Migda
Janusz Migda
Małgorzata Zdanowicz

Abstract. A second-order nonlinear neutral difference equation with a quasi-difference is studied. Sufficient conditions are established under which for every real constant there exists a solution of the considered equation convergent to this constant.

Keywords: second-order difference equation, asymptotic behavior, quasi-differences, Krasnoselskii's fixed point theorem.

Mathematics Subject Classification: 39A10, 39A22, 39A30.

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• Communicated by Marek Galewski.
• Revised: 2018-04-15.
• Accepted: 2018-06-07.
• Published online: 2018-08-07.