On the asymptotic behavior of solutions of higher order nonlinear difference equations

Asymptotic behavior of solutions of discrete Volterra equations

“…The proof is complete. Theorem 3.1 generalizes the results obtained by J. Popenda [22] and M. Migda, J. Migda [18].…”

“…The results devoted to the study of asymptotically polynomial solutions of ordinary difference equations can be found, for example, in [15,17,18,22] or [23]. In 1986, Popenda [22] gave sufficient conditions under which for any polynomial of degree at most m − 1, there exists a solution x of the form (1.1) with s = 0 for a difference equation…”

“…Note that we extend the range of s from (−∞, 0] to (−∞, m − 1]. 18) |f (n, t)| ≤ g |t| n m−1 for (n, t) ∈ N × R, Using the condition: K(j, i) = 0 for i > j and (3.18), we obtain…”

Stability in Functional Difference Equations Using Fixed Point Theory

“…For more on the use of Lyapunov functional we ask the reader to consult with [1], [2], [3], [6], [12], [13], [15]. For more recent results on the existence of periodic solutions in difference equations we refer the reader to [4], [7], [5], [9], and [14].…”

Approximative solutions to difference equations of neutral type

“…In the cycle of papers [10], [14][15][16][17][18][19][20] a new method in the study of asymptotic properties of solutions to difference equations is presented. This method, based on using the iterated remainder operator, allows us to control the degree of approximation.…”