Oscillation analysis for nonlinear difference equation with non-monotone arguments

Well-Defined Solutions of a Three-Dimensional System of Difference Equations

“…that is the sequence ( ) ≥−1 is periodic with period 12 and takes the form 4 , − −1 + (5) , − 0 + (0) , − 1 + (1) , − 2 + (2) , − 3 + (3) , − 4 + (4) , −1 , 0 , … ).…”

“…Difference equations and their systems are related to many real life models in different branches of modern science such as biology, physics, economics, etc, in [1,2]. This is due to the fact that these models are expressed by discrete equations and this explain why difference equations and their systems have attracted the attention of many researchers in recent years in [3][4][5][6]. One of the most popular subject associated with difference equations and their system, especially the non-linear ones, is to examine their solvability and the behavior of their solutions in .…”

Oscillation criteria for first-order dynamic equations with nonmonotone delays

“…Assume that f : T → R is rd-continuous, g : T → R is nonincreasing and τ :T → T is nondecreasing. If b < u, then σ(u) b f (s)g(τ (s))∆s ≥ g(τ (u)) σ(u) b f (s)∆s.The following result is easily obtained by using the similar way in the proof of Lemma 2.3 in[24]. Assume that (2.1) holds and α > 0.…”

Some conditions for the oscillation of second-order differential equations with several mixed delays

“…Finally, we refer the interested reader to the following paper and to the references therein for some recent results on the oscillation theory for ordinary differential equations of several orders [11][12][13][14][15][16][17][18].…”