Oscillatory and asymptotic properties of solutions of even order neutral difference equations

Oscillation criteria for second-order nonlinear neutral difference equations of mixed type

“…However, there are few results available in the literature regarding the oscillatory properties of neutral difference equations of mixed type, see for example [1][2][3][4][5][6][7][8]. Motivated by the above observation, in this article we establish some new oscillation criteria for the Equation (E ± ) which generalize some of the results obtained in [1][2][3][5][6][7].…”

“…The oscillation, nonoscillation and asymptotic behavior of solutions of Equation (E ± ), when b = 0 and p n ≡ 0 or a = 0 and p n ≡ 0 or b = 0 and q n ≡ 0 have been considered by many authors, see for example [1][2][3][4] and the reference cited therein. However, there are few results available in the literature regarding the oscillatory properties of neutral difference equations of mixed type, see for example [1][2][3][4][5][6][7][8].…”

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.…”

“…By a solution of (E) we mean a sequence x: N(0) → R satisfying (E) for all large n. Asymptotic properties of solutions to neutral equations were investigated in many papers, see, for example, [1][2][3][4][5][6][7][8][9], [11][12][13].…”

Asymptotically polynomial solutions to difference equations of neutral type

“…These studies tend in several directions. For example, the papers [3], [15], [17] and [25] are devoted to the classification of solutions. In [8], [9], [11] and [24] where studied solutions with prescribed asymptotic behavior.…”