New Comparison Theorems for the Nth Order Neutral Differential Equations with Delay Inequalities

Abstract

In this work, we present a new technique for the oscillatory properties of solutions of higher-order differential equations. We set new sufficient criteria for oscillation via comparison with higher-order differential inequalities. Moreover, we use the comparison with first-order differential equations. Finally, we provide an example to illustrate the importance of the results.

Amended oscillation criteria for second-order neutral differential equations with damping term

“…Let (D 2 ) hold. As in the proof of Lemma 2, we arrive at (19). Integrating (19) from t to ∞, we find…”

“…Proof For the proof of this lemma, it suffices to use (19) [from the proof of Lemma 4] instead of (17) in the proof of Theorem 2.…”

“…[10,11] developed the oscillation criteria. The results in [12][13][14][15][16][17][18][19][20][21] dealt with the issue of oscillation of equations of higher order. For differential equations with damping, we present the following results that are closely related to this paper.…”

New Aspects for Non-Existence of Kneser Solutions of Neutral Differential Equations with Odd-Order

“…There are many authors who studied the problem of oscillation of differential equations of a different order and presented many techniques in order to obtain criteria for oscillation of the studied equations, for example, [1][2][3][4][5][6][7][8][9][10][11][12].…”

Oscillatory Properties of Odd-Order Delay Differential Equations with Distribution Deviating Arguments

“…Oscillatory behavioral nature of solutions of various classes of neutral and delay differential equations is of great interest, and often encountered in applied problems in natural sciences, technology, and engineering, see [1,2]. Recently it has been noticed the rising interest of many researchers and papers in studying the qualitative properties of different classes of linear and non-linear differential equations, see [1][2][3][4][5][6][7][8][9][10][11][12][13][14].…”