**Volume 17, Issue 2, pp 194-199**

**Publication Date**: 2017-06-15

http://dx.doi.org/10.22436/jmcs.017.02.01

Haixia Wang - School of Economics, Ocean University of China, Qingdao, Shandong 266100, P. R. China.

Guojuan Chen - School of Informatics, Linyi University, Linyi, Shandong 276005, P. R. China.

Ying Jiang - Qingdao Technological University, Feixian, Shandong 273400, P. R. China.

Cuimei Jiang - Qingdao Technological University, Feixian, Shandong 273400, P. R. China.

Tongxing Li - School of Informatics, Linyi University, Linyi, Shandong 276005, P. R. China.

We consider the asymptotic behavior of solutions to a class of third-order neutral differential equations with distributed deviating arguments. Our criteria extend the related results reported in the literature. An illustrative example is included.

Asymptotic behavior, neutral differential equation, third-order, distributed deviating argument, oscillation.

[1] R. P. Agarwal, M. Bohner, T.-X. Li, C.-H. Zhang, Hille and Nehari type criteria for third-order delay dynamic equations, J. Difference Equ. Appl., 19 (2013), 1563–1579.

[2] R. P. Agarwal, M. Bohner, T.-X. Li, C.-H. Zhang, Oscillation of third-order nonlinear delay differential equations, Taiwanese J. Math., 17 (2013), 545–558.

[3] R. P. Agarwal, M. Bohner, T.-X. Li, C.-H. Zhang, A Philos-type theorem for third-order nonlinear retarded dynamic equations, Appl. Math. Comput., 249 (2014), 527–531.

[4] R. P. Agarwal, M. Bohner, S.-H. Tang, T.-X. Li, C.-H. Zhang, Oscillation and asymptotic behavior of third-order nonlinear retarded dynamic equations, Appl. Math. Comput., 219 (2012), 3600–3609.

[5] B. Bacul´ıkov´a, J. Dˇzurina, Oscillation of third-order neutral differential equations, Math. Comput. Modelling, 52 (2010), 215–226.

[6] M. Bohner, S. R. Grace, I. Jadlovsk´a, Oscillation criteria for third-order functional differential equations with damping, Electron. J. Differential Equations, 2016 (2016), 15 pages.

[7] M. Bohner, S. R. Grace, I. Sa˘ger, E. Tunc¸, Oscillation of third-order nonlinear damped delay differential equations, Appl. Math. Comput., 278 (2016), 21–32.

[8] T. Candan, Oscillation criteria and asymptotic properties of solutions of third-order nonlinear neutral differential equations, Math. Methods Appl. Sci., 38 (2015), 1379–1392.

[9] Z. Doˇsl´a, P. Liˇska, Oscillation of third-order nonlinear neutral differential equations, Appl. Math. Lett., 56 (2016), 42–48.

[10] J. Dˇzurina, R. Kotorov´a, Properties of the third order trinomial differential equations with delay argument, Nonlinear Anal., 71 (2009), 1995–2002.

[11] Y.-L. Fu, Y.-Z. Tian, C.-M. Jiang, T.-X. Li, On the asymptotic properties of nonlinear third-order neutral delay differential equations with distributed deviating arguments, J. Funct. Spaces, 2016 (2016), 5 pages.

[12] J. K. Hale. Theory of functional differential equations, Second edition. Applied Mathematical Sciences, Springer- Verlag, New York-Heidelberg, (1977).

[13] C.-M. Jiang, Y. Jiang, T.-X. Li, Asymptotic behavior of third-order differential equations with nonpositive neutral coefficients and distributed deviating arguments, Adv. Difference Equ., 2016 (2016), 14 pages.

[14] Y. Jiang, C.-M. Jiang, T.-X. Li, Oscillatory behavior of third-order nonlinear neutral delay differential equations, Adv. Difference Equ., 2016 (2016), 12 pages.

[15] Y. Jiang, T.-X. Li, Asymptotic behavior of a third-order nonlinear neutral delay differential equation, J. Inequal. Appl., 2014 (2014), 7 pages.

[16] T.-X. Li, Y. V. Rogovchenko, Asymptotic behavior of an odd-order delay differential equation, Bound. Value Probl., 2014 (2014), 10 pages.

[17] T.-X. Li, Y. V. Rogovchenko, Asymptotic behavior of higher-order quasilinear neutral differential equations, Abstr. Appl. Anal., 2014 (2014), 11 pages.

[18] T.-X. Li, C.-H. Zhang, Properties of third-order half-linear dynamic equations with an unbounded neutral coefficient, Adv. Difference Equ., 2013 (2013), 8 pages.

[19] T.-X. Li, C.-H. Zhang, G.-J. Xing, Oscillation of third-order neutral delay differential equations, Abstr. Appl. Anal., 2012 (2012), 11 pages.

[20] M. T. S¸enel, N. Utku, Oscillation behavior of third-order nonlinear neutral dynamic equations on time scales with distributed deviating arguments, Filomat, 28 (2014), 1211–1223.

[21] M. T. S¸enel, N. Utku, Oscillation criteria for third-order neutral dynamic equations with continuously distributed delay, Adv. Difference Equ., 2014 (2014), 15 pages.

[22] Y.-Z. Tian, Y.-L. Cai, Y.-L. Fu, T.-X. Li, Oscillation and asymptotic behavior of third-order neutral differential equations with distributed deviating arguments, Adv. Difference Equ., 2015 (2015), 14 pages.