Oscillatory of Third-Order Neutral Differential Equations with Continuously Distributed Mixed Arguments

Authors

Nagehan Kılınc Gecer, Department of Mathematics, Faculty of Arts and Sciences,Ahi Evran University, 40100, Kırs¸ehir, TurkeyFollow
Pakize Temtek, Department of Mathematics, Faculty of Sciences, Erciyes University, 38039, Kayseri, TurkeyFollow

Author Country (or Countries)

Turkey

Abstract

It is the purpose of this paper to give oscillation criteria for the third-order neutral differential equation with continuously distributed mixed arguments r(t) 􀀀 [x(t)+ Z b a p(t,m)x[t (t,m)]dm] ′′ g ′ + Z d c q1(t,x ) f (x[f1(t,x )])dx + Z d c q2(t,h)g(x[f2(t,h)])dh = 0, where g > 0 is a quotient of odd positive integers. By using a generalized Riccati transformation and integral averaging technique, we establish some new sufficient conditions which ensure that every solution of this equation oscillates or converges to zero.

Digital Object Identifier (DOI)

http://dx.doi.org/10.18576/amis/100531

Recommended Citation

Kılınc Gecer, Nagehan and Temtek, Pakize (2016) "Oscillatory of Third-Order Neutral Differential Equations with Continuously Distributed Mixed Arguments," Applied Mathematics & Information Sciences: Vol. 10: Iss. 5, Article 31.
DOI: http://dx.doi.org/10.18576/amis/100531
Available at: https://digitalcommons.aaru.edu.jo/amis/vol10/iss5/31