An Oscillation Criterion for First Order Difference Equations

Upper and lower limit oscillation conditions for first-order difference equations

“…In 2016, Öcalan [15], when (τ (n)) is not necessarily monotone, established the following result; if…”

“…In recent years, there has been much research activity concerning the oscillation and non-oscillation of solutions of delay differential and difference equations. For these oscillatory and non-oscillatory results, we refer, for instance [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19].…”

“…In 2016, Öcalan [15], when is not necessarily monotone, established the following result; if where , , then all solutions of (1.1) are oscillatory.…”

On an approach to the analysis of oscillatory solutions of nonlinear delay difference equations

“…In 1989 Erbe and Zhang 1 and Ladas et al 2 established some criteria for the oscillatory solution of () with constant delay. In addition, in 1991 Philos, 3 in 1998 Zhang and Tian, 4,5 in 2006 Yan, Meng and Yan, 6 in 2011 Braverman and Karpuz, 7 in 2014 Stavroulakis, 8 in 2016 Öcalan, 9 and in 2019 Chatzarakis and Jadlovská 10 studied equation () and obtained some oscillation results.…”

“…The question of obtaining oscillation criteria for all solutions of difference equations has been the important subject of numerous research; see, for instance previous research, [1][2][3][4][5][6][7][8][9][10][11][12][15][16][17][18][19][20][21] and the references cited therein. The majority of these publications are concerned with the exceptional issue of nondecreasing arguments, while a small number of them are concerned with the more general case of delays that are not always monotone.…”