Asymptotic behavior of solutions of the mth-order nonhomogeneous difference equations

AbstractAsymptotic behavior of solutions of the mth-order difference equation of the form (E1) Δmxn + ƒ(n, xn,…, Δm−1xn) = hn and some special case (E2) of these equation are investigated

Asymptotic behavior of solutions of discrete Volterra equations

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

Some stability conditions for scalar Volterra difference equations

New explicit stability results are obtained for the following scalar linear difference equation $$x(n+1)-x(n)=-a(n)x(n)+\sum_{k=1}^n A(n,k)x(k)+f(n)$$ and for some nonlinear Volterra difference equations

Nonoscillatory Solutions to Second-Order Neutral Difference Equations

We study asymptotic behavior of nonoscillatory solutions to second-order neutral difference equation of the form: Δ ( r n Δ ( x n + p n x n − τ ) ) = a n f ( n , x n ) + b n . The obtained results are based on the discrete Bihari type lemma and a Stolz type lemma

Asymptotic properties of the solutions of the second order difference equation

summary:Asymptotic properties of the solutions of the second order nonlinear difference equation (with perturbed arguments) of the form $$\Delta ^2 x_n = a_n \varphi (x_{n+k})$$ are studied

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

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

Nonoscillatory Solutions to Second-Order Neutral Difference Equations

We study asymptotic behavior of nonoscillatory solutions to second-order neutral difference equation of the form: Δ ( r n Δ ( x n + p n x n − τ ) ) = a n f ( n , x n ) + b n . The obtained results are based on the discrete Bihari type lemma and a Stolz type lemma