Oscillatory and nonoscillatory behavior of second-order neutral delay difference equations II

Oscillation Criteria of Comparison Type for Second Order Difference Equations

“…For example, we refer the reader to the papers [1]- [3], [5]- [15] and the references cited therein where several particular cases of (1.2) have been discussed. For example, we refer the reader to the papers [1]- [3], [5]- [15] and the references cited therein where several particular cases of (1.2) have been discussed.…”

Oscillation Criteria for Second Order Neutral Difference Equations With Negative Neutral Term

“…A solution of equation (1) is said to be oscillatory if it is neither eventually positive nor eventually negative, and it is nonoscillatory otherwise. From a review of the literature, it is known that there are many results available on the oscillatory and asymptotic behavior of solutions of equation (1) when the neutral term is nonnegative, i.e., p n ≤ 0; see, for example, [1,2,3,4,6,7] and the references cited therein. However, there are very few results available on the oscillatory behavior of solutions of equation (1) when the neutral term is negative; see, for example, [1,2,5,8,9,10,11,12], and the references therein.…”

Necessary Conditions for the Solutions of Second Order Non-linear Neutral Delay Difference Equations to Be Oscillatory or Tend to Zero

“…In recent years, many authors have shown interest in the oscillation of neutral delay difference equations (NDDEs in short). For recent results and references, see the monograph by Agarwal [4], the papers [5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20][21][22], and the references cited there in. In this paper, neither (H0) nor (H1) is assumed for obtaining positive solution of (1.2).…”