Oscillation and Nonoscillation of Second Order Differential Equations with Deviating Arguments

Oscillation Criteria for Delay and Advanced Differential Equations with Nonmonotone Arguments

“…The oscillation criteria established in this paper all depend on 0 (see, e.g., (37) and (71)) in contrast to the conditions obtained in [15,16] and in [17, for m = 1]. In fact, the left-hand side of conditions (37) and (71) depends on 0 , which is not the case with the left-hand side of conditions (20) and (21). Since 0 > 1 when ∈ (0, 1/ ], it is obvious that 0 ( ) = 0 ( ) > ( ) = 0 ( ) .…”

“…Consequently, the left-hand side of conditions (37) and (71) is greater than the corresponding parts of (20) and (21), respectively. This is the reason why the conditions in this paper improve on all known conditions mentioned in Section 2.…”

“…and established sufficient oscillation conditions. Those conditions can lead to (20) and (21) when = 1.…”

Iterative oscillation tests for differential equations with several non-monotone arguments

“…In the last few decades, oscillatory behavior and stability of first-order differential equations with deviating arguments have been extensively studied, see, for example, papers [3]- [6], [9]- [17], [19]- [25] and references cited therein. For the general oscillation theory of differential equations the reader is referred to the monographs [1,7,8,18].…”

Oscillations of differential equations with several non-monotone advanced arguments

“…[1] Today there exists an extensive literature on the oscillation theory of advanced type differential equations. See, for example, [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18] and the references cited therein.…”