Oscillation of Forced Nonlinear Neutral Delay Difference Equations of First Order

Oscillation of higher order neutral functional difference equations with positive and negative coefficients

“…Our results hold good for G(u) ≡ u, f n ≡ 0 and u n ≡ 0. The last but not the least, this paper corrects, generalizes and improves some of the results of [11,12,14,16,17,19,21].…”

“…In recent years, several papers on oscillation of solutions of neutral delay difference equations have appeared; (cf. [1,2], [11]- [22]) and the references cited therein. In literature we find that (1.1) is very rarely studied.…”

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).…”

“…In this paper, neither (H0) nor (H1) is assumed for obtaining positive solution of (1.2). However, several authors use these conditions while they attempted the same problem for neutral equations of any order; see [6,[12][13][14][15][16][17][18][19][20][21][22]. To the best of our knowledge, no result regarding positive solutions of neutral equations (both differential and difference equations) of any order with p n ≡ −1 is available in the literature.…”

“…Even the papers written specially for p n = ±1 do not have such a result [13,14,18,20]. For difference equations, most ranges are covered in [12,13,15], but there is no result for p n = ±1. In this paper, we have covered all ranges of p n including those missing in [12,13,15].…”