TY  - JOUR
ID  - Migda2016
LB  - Migda2016
AU  - Migda, Janusz
AU  - Migda, Małgorzata
TI  - Asymptotic behavior of solutions of discrete Volterra equations
ST  - Asymptotic behavior of solutions of discrete Volterra equations
JO  - Opuscula Math.
JA  - Opuscula Math.
JF  - Opuscula Mathematica
PY  - 2016
VL  - 36
IS  - 2
SP  - 265
EP  - 278
DO  - http://dx.doi.org/10.7494/OpMath.2016.36.2.265
UR  - http://dx.doi.org/10.7494/OpMath.2016.36.2.265
AB  - 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.
KW  - Volterra difference equation
KW  - prescribed asymptotic behavior
KW  - asymptotically polynomial solution
KW  - asymptotically periodic solution
KW  - bounded solution
SN  - 1232-9274
ER  -