Abstract
In this article, we study a class of non-linear neutral delay differential equations of third order. We first prove criteria for non-existence of non-Kneser solutions, and criteria for non-existence of Kneser solutions. We then use these results to provide criteria for the under study differential equations to ensure that all its solutions are oscillatory. An example is given that illustrates our theory.
Highlights
The interest in studying delay differential equations is caused by the fact that they appear in models of several areas in science
Properties of delay differential equations are used in the study of singular differential equations of fractional order, see [7,8,9], and other type of fractional operators such as the fractional nabla applied to difference equations where the memory effect appears, see [10,11]
For more recent results of oscillatory properties of solutions of Neutral time delay differential equations (NDDEs) and non-linear differential equations, we refer the reader to the works [22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55]
Summary
The interest in studying delay differential equations is caused by the fact that they appear in models of several areas in science. For more recent results of oscillatory properties of solutions of NDDEs and non-linear differential equations, we refer the reader to the works [22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55]. All functional inequalities and properties such as increasing, decreasing, positive, and so on, are assumed to hold eventually, i.e., they are satisfied for all t ≥ t1 ≥ t0 , where t1 large enough
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