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Browsing by Author "Migda, Janusz"

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    Item type:Article, Access status: Open Access ,
    Asymptotic behavior of solutions of discrete Volterra equations
    (2016) Migda, Janusz; Migda, Małgorzata
    We consider the nonlinear discrete Volterra equations of non-convolution type $\Delta^m x_n=b_n+\sum\limits_{i=1}^{n}K(n,i)f\left(i,x_i\right), \quad n\geq 1.$ We present sufficient conditions for the existence of solutions with prescribed asymptotic behavior, especially asymptotically polynomial and asymptotically periodic solutions. We use $\operatorname{o}(n^s)$, for a given nonpositive real $s$, as a measure of approximation. We also give conditions under which all solutions are asymptotically polynomial.
  • thumbnail.journal.alt
    Item type:Article, Access status: Open Access ,
    On the convergence of solutions to second-order neutral difference equations
    (Wydawnictwa AGH, 2019) Migda, Małgorzata; Migda, Janusz; Zdanowicz, Małgorzata
    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.