Oscillatory Behavior of Third Order Nonlinear Neutral Differential Equations

Abstract

In this paper, we study the oscillatory behavior of the following neutral differential equation [(a(t)Sufficient conditions are obtained so that every every solution is either oscillatory or converges to zero. In particular. we extend the results obtained in [ 6 ] by not assuming a(t) is non-decreasing. Examples are provided to illustrate the main results.

Oscillation results for second order half-linear neutral delay differential equations with "maxima"

“…Therefore, the results presented in this paper improve and complement to the results in [1,4,6,16,17,20].…”

“…However, the oscillation theory of neutral differential equations with "maxima" received less attention eventhough such equations arise in many applications, see for example [1,3,4,5,6,15,16,17,18,20], and the references contained therein.…”

“…In [4,6,17,20], the authors established some conditions for all solutions of equation are oscillatory. Therefore, the results presented in this paper improve and complement to the results in [1,4,6,16,17,20].…”

Oscillatory Properties of Third-Order Neutral Delay Differential Equations with Noncanonical Operators

“…A further improvement of these results was presented in [17]. Depending on various ranges of p, a variety of results for property A of (1), its generalizations or particular cases, exist in the literature, see, e.g., [13,[18][19][20][21][22][23][24][25][26][27] and the references cited therein. Among them, only the work in [13] considered (1) in noncanonical form with 0 ≤ p < 1.…”

Oscillatory and Asymptotic Behavior of Third Order Half-linear Neutral Dierential Equation with \Maxima"

“…where  is the quotient of odd positive integers, subject to the following conditions: In recent years there has been great attention denoted to the oscillatory and asymptotic behavior of third order neutral differential equations without maxima, see [1,7,8,9,13,14], and the references contained therein. However few results are available on the oscillatory behavior of third order differential equation with "maxima", see [2,3,4,5,6].…”