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

Abstract

Some new oscillatory and asymptotic properties of solutions of neutral differential equations with odd-order are established. Through the new results, we give sufficient conditions for the oscillation of all solutions of the studied equations, and this is an improvement of the relevant results. The efficiency of the obtained criteria is illustrated via example.

Even-order differential equation with continuous delay: nonexistence criteria of Kneser solutions

“…This is due to the existence of many important applications of this theory in various fields of applied science, see [18,19]. In the last decade, it is easy to notice the new research movement that aims to improve and develop the criteria for oscillations of DEs of different orders, see [3][4][5] and [9][10][11][12][13][14][15][16][17].…”

New Asymptotic Properties of Positive Solutions of Delay Differential Equations and Their Application

“…Bohner et al [7], Grace et al [8], and Moaaz et al [9,10] also extended this evolution to DDEs of the neutral type. On the other hand, Džurina et al [11,12] and Moaaz et al [13] dealt by different methods with the asymptotic properties of the solutions of DDEs of the odd-order.…”

Criteria for the Oscillation of Solutions to Linear Second-Order Delay Differential Equation with a Damping Term

“…Oscillation theory is a branch of the qualitative theory of functional differential equations, which is concerned with the study of the oscillatory and non-oscillatory behavior of solutions to differential equations. The growing interest and development in the oscillation theory of delay differential equations can be seen through the works [4][5][6][7].…”