Oscillatory behavior of third-order nonlinear differential equations with mixed neutral terms

Yıl 2021, Cilt: 50 Sayı: 3, 833 - 844, 07.06.2021

Said R. Grace John R. Graef , Ercan Tunc

https://doi.org/10.15672/hujms.693738

Öz

This paper deals with the oscillation of third-order nonlinear differential equations with neutral terms involving positive and negative nonlinear parts. An example is provided to illustrate the results.

Anahtar Kelimeler

oscillation, third order, mixed neutral term, neutral differential equations

Kaynakça

• [1] R.P. Agarwal, S.R. Grace and D. O’Regan, Oscillation Theory for Second Order Lin- ear, Half-Linear, Superlinear and Sublinear Dynamic Equations, Kluwer, Dordrecht, 2010.
• [2] R.P. Agarwal, S.R. Grace and D. O’Regan, Oscillation Theory for Difference and Functional Differential Equations, Kluwer, Dordrecht, 2010.
• [3] R.P. Agarwal, M. Bohner, T. Li and C. Zhang, A new approach in the study of oscillatory behavior of even-order neutral delay differential equations, Appl. Math. Comput. 225, 787–794, 2013.
• [4] R.P. Agarwal, M. Bohner, T. Li and C. Zhang, Oscillation of second-order differential equations with a sublinear neutral term, Carpathian J. Math. 30, 1–6, 2014.
• [5] D.D. Bainov and D.P. Mishev, Oscillation Theory for Neutral Differential Equations with Delay, Adam Hilger, Bristol, 1991.
• [6] O. Bazighifan, Kamenev and Philos-types oscillation criteria for fourth-order neutral differential equations, Adv. Differ. Equ. 2020, No. 201, 2020.
• [7] O. Bazighifan, On the oscillation of certain fourth-order differential equations with p-Laplacian like operator, Appl. Math. Comput. 386, 125475, 2020.
• [8] O. Bazighifan, Oscillatory applications of some fourth-order differential equations, Math. Methods Appl. Sci., https://doi.org/10.1002/mma.6694.
• [9] O. Bazighifan and H. Ramos, On the asymptotic and oscillatory behavior of the solu- tions of a class of higher-order differential equations with middle term, Appl. Math. Lett. 107, 106431, 2020.
• [10] S.J. Bilchev, M.K. Grammatikopoulos and I.P. Stavroulakis, Oscillations of second- order neutral differential equations with deviating arguments, in: Oscillation and Dy- namics in Delay Equations, Proc. Spec. Sess. AMS, San Francisco/CA (USA) 1991, Contemp. Math. 129, 1–21, 1992.
• [11] J. Džurina and R. Kotorová, Properties of the third order trinomial differential equa- tions with delay argument, Nonlinear Anal. 71, 1995–2002, 2009.
• [12] J.-G. Dong, Oscillation behavior of second order nonlinear neutral differential equa- tions with deviating arguments, Comput. Math. Appl. 59, 3710–3717, 2010.
• [13] L.H. Erbe, Q. Kong and B.G. Zhang, Oscillation Theory for Functional Differential Equations, Dekker, New York, 1995.
• [14] S.R. Grace, R.P. Agarwal and D. O’Regan, A selection of oscillation criteria for second-order differential inclusions, Appl. Math. Lett. 22, 153–158, 2009.
• [15] S.R. Grace, E. Akın and C.M. Dikmen, On the oscillation of second order nonlin- ear neutral dynamic equations with distributed deviating arguments on time scales, Dynam. Systems Appl. 23, 735–748, 2014.
• [16] S.R. Grace, M. Bohner and R.P. Agarwal, On the oscillation of second-order half- linear dynamic equations, J. Differ. Equ. Appl. 15, 451–460, 2009.
• [17] S.R. Grace, J.R. Graef and M.A. El-Beltagy, On the oscillation of third order neutral delay dynamic equations on time scales, Comput. Math. Appl. 63, 775–782, 2012.
• [18] S.R. Grace, J.R. Graef and E. Tunç, Oscillatory behavior of third order nonlinear differential equations with a nonlinear nonpositive neutral term, J. Taibah Univ. Sci. 13, 704–710, 2019.
• [19] S.R. Grace, R.P. Agarwal, M. Bohner, and D. O’Regan, Oscillation of second-order strongly superlinear and strongly sublinear dynamic equations, Comum. Nonlinear Sci. Numer. Simulat. 14, 3463–3471, 2009.
• [20] S.R. Grace, R.P. Agarwal, B. Kaymakçalan and W. Sae-jie, Oscillation theorems for second order nonlinear dynamic equations, J. Appl. Math. Comput. 32, 205–218, 2010.
• [21] J.R. Graef and S.H. Saker, Oscillation theory of third-order nonlinear functional dif- ferential equations, Hiroshima Math. J. 43, 49–72, 2013.
• [22] I. Györi and G. Ladas, Oscillation Theory of Delay Differential Equations with Ap- plications, Clarendon Press, Oxford, 1991.
• [23] G.H. Hardy, I.E. Littlewood and G. Polya, Inequalities, Reprint of the 1952 edition, Cambridge University Press, Cambridge, 1988.
• [24] R.G. Koplatadze and T.A. Chanturiya, Oscillating and monotone solutions of first- order differential equations with deviating argument (in Russian), Differ. Uravn. 18, 1463–1465, 1982.
• [25] G. Ladas and I.P. Stavroulakis, Oscillation caused by several retarded and advanced arguments, J. Differ. Equations, 44, 134–152, 1982.
• [26] T. Li, Yu. V. Rogovchenko and C. Zhang, Oscillation results for second-order non- linear neutral differential equations, Adv. Differ. Equ. 2013, Article ID: 336, 13pp, 2013.
• [27] H. Qin, N. Shang and Y. Lu, A note on oscillation criteria of second order nonlinear neutral delay differential equations, Comput. Math. Appl. 56, 2987–2992, 2008.
• [28] I.P. Stavroulakis, Oscillations of mixed neutral equations, Hiroshima Math. J. 19, 441–456, 1989.
• [29] J.S.W. Wong, Necessary and sufficient conditions for oscillation of second order neu- tral differential equations, J. Math. Anal. Appl. 252, 342–352, 2000.