Oscillatory and asymptotic behavior of third-order nonlinear neutral differential equations with unbounded neutral coefficients
ZENG Yunhui1, WANG Zhihong1, WANG Anning1, LUO Liping1, YU Yuanhong2
1.College of Mathematics and Statistics, Hengyang Normal University, Hengyang 421008, Hunan Province, China 2.Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190, China
Abstract：The objective of this paper is to study oscillatory and asymptotic behaviors of solutions of third-order nonlinear neutral differential equations with unbounded neutral coefficients.By introducing the parameter function and the generalized Riccati transformations,and jointly applying the differential inequality technique and integral averaging technique,we establish some new sufficient conditions which ensure that every solution of the equations oscillates or converges to zero.The results obtained can be easily extended to more general neutral differential equations as well as neutral dynamic equations on the scales. An example is provided to illustrate new results.
1 AGARWAL R P，GRACE S R，O’REGAN D.Oscillation Theory for Difference and Functional Differential Equations［M］.Dordrecht：Kluwer Academic Publishers，2000. 2 CANDAN T.Oscillatory behavior of second-order nonlinear functional differential equations with distributed deviating arguments［J］.Applied Mathematics and Computation，2015，262：199-203. 3 GRAEF J R，SAKER S H. Oscillation theory of third-order nonlinear functional differential equations［J］.Hiroshima Mathematical Journal，2013，43（1）：49-72. DOI：10.32917/hmj/1368217950 4 BACULIKOVA B，DZURINA J. Oscillation of third-order neutral differential equations［J］.Mathematical and Computer Modelling，2010，52（1/2）：215-226.DOI：10.1016/j.mcm.2010.02.011 5 THANDAPANI E，SAVITHRI R，GRAEF J.Oscillatory properties of third order neutral delay differential equations［J］.Discrete & Continuous Dynamical Systems，2003，9（special）：342-350. 6 LI T X，ZHANG C H，XING G J. Oscillation of third-order neutral delay differential equations［J］.Abstract & Applied Analysis，2012，2012：569201.DOI：10.1155/2012/569201 7 MOHAMAD H A.Oscillation of linear neutral differential equation of third order［J］. Iraqi Sci，2009，50（4）：543-547. 8 SOLIMAN A A，SALLAM R A，ELBITAR A，et al.Oscillation criteria of third order nonlinear neutral differential equations［J］.International Journal of Applied Mathematical Research，2012，1（3）：268-281. DOI：10.14419/ijamr.v1i3.95 9 MOAAZ O，ELABBASY E M.On the asymptotic behavior of third-order nonlinear functional differential equations［J］.Serdica Mathematical Journal，2016，42（2）：157-174. 10 KIGURADGE I T，CHANTURIYA T A.Asymptotic Properties of Solutions of Nonautonomous Ordinary Differential Equations［M］. Dordreecht：Kluwer Academic Publishers，1993. 11 LI T X，THANDAPANI E. Oscillation of solutions to odd-order nonlinear neutral functional differential equations［J］.Electron Journal Differential Equations，2011，23：1-12. 12 THANDAPANI E，LI T X.On the oscillation of third-order quasi-linear neutral functional differential equations［J］.Archivum Mathematicum （BRNO），2011，47：181-199. DOI：10.2478/s12175-013-0189-z 13 LI T X，THANDAPANI E.Oscillation theorems for odd-order neutral differential equations［J］.Funct Differ Equ，2012，19：147-155. 14 GRAEF J R，TUN E，GRACE S R.Oscillatory and asymptotic behavior of a third-order nonlinear neutral differential equations［J］. Opuscula Mathematica，2017，37（6）：839-852. DOI：10.7494/OpMath.2017.37.6.839 15 CHATZARAKIS G E，GRACE S R，JADLOVSK? I，et al.Oscillation criteria for third-order Emden-Fowler differential equations with unbounded neutral coefficients［J］.Complexity，2019，2019：5691758.DOI：10.1155/2019/5691758 16 LI T X，ZHANG C H.Properties of third-order half-linear dynamic equations with an unbounded neutral coefficient［J］.Advances in Difference Equations，2013（1）：333. DOI：10.1186/1687-1847-2013-333 17 ZHANG Z Y，WANG X X，YU Y H.Oscillation of third-order half-linear neutral differential equations with distributed delay［J］.Acta Mathematicae Applicatae Sinica，2015，38（3）：450-459.DOI：10.2478/s12175-008-0068-1
2021, Vol. 48 
