Oscillation Results for Third-Order Quasi-Linear Emden-Fowler Differential Equations with Unbounded Neutral Coefficients

George E. Chatzarakis; Radhakrishnan Srinivasan; Ethiraju Thandapani

doi:10.2478/tmmp-2021-0028

.blurhash-client-img { display: none !important; }

Oscillation Results for Third-Order Quasi-Linear Emden-Fowler Differential Equations with Unbounded Neutral Coefficients

Tatra Mountains Mathematical Publications

Volume 80 (2021): Issue 3 (December 2021)

By: George E. Chatzarakis, Radhakrishnan Srinivasan and Ethiraju Thandapani

Open Access

|Jan 2022

Abstract

Some new oscillation criteria are obtained for a class of thirdorder quasi-linear Emden-Fowler differential equations with unbounded neutral coefficients of the form $(a (t) {(z ″ (t))}^{α})' + f (t) y^{λ} (g (t)) = 0,$ \[(a(t){(z(t))^\alpha })' + f(t){y^\lambda }(g(t)) = 0,\] where z(t) = y(t) + p(t)y(σ(t)) and α, λ are ratios of odd positive integers. The established results generalize, improve and complement to known results.

References

[1] AGARWAL, R. P.—GRACE, S. R.—REGAN, D. O.: Oscillation Theory for Difference and Functional Differential Equations. Kluwer Academic, Dordrecht, 2000.10.1007/978-94-015-9401-1
Search in Google Scholar Back to article
[2] CHATZARAKIS, G. E.—GRACE, S. R.—JADLOVSKA, I.—LI, T.—E. TUNC, E.: Oscillation criteria for third order Emden-Fowler differential equations with unbounded neutral coefficients, Complexity 2019, Article ID 5691758, 7 p.10.1155/2019/5691758
Search in Google Scholar Back to article
[3] SAKAMOTO, T.—TANAKA, S.: Eventually positive solutions of first order nonlinear differential equations with a deviating argument, Acta Math. Hungar. 127 (2010), 117–133.10.1007/s10474-010-9064-3
Search in Google Scholar Back to article
[4] TANG, X. H.: Oscillation for first order superlinear delay differential equations, J. London Math. Soc. 65 (2002), no. 1, 115–122.10.1112/S0024610701002678
Search in Google Scholar Back to article
[5] THANDAPANI, E.—LI, T.: On the oscillation of third order quasilinear neutral functional differential equations, Arch. Math. 47 (2011), 181–199.
Search in Google Scholar Back to article
[6] LI, T.—ZHANG, C.—XING, G.: Oscillation of third order neutral delay differential equations, Abast. Appl. 2012, Article ID 569201, 11 p.10.1155/2012/569201
Search in Google Scholar Back to article
[7] BACULIKOVÁ, B.—DZURINA, J.: Oscillation of third-order neutral differential equations, Math. Comput. Model. 52 (2010), 215–226.10.1016/j.mcm.2010.02.011
Search in Google Scholar Back to article
[8] BACULIKOVÁ, B.—RANI, B.—SELVARANGAM, S.—THANDAPANI, E.: Properties of Kneser’s solutions for half-linear third order neutral differential equations, Acta Math. Hungar. 152 (2017), 525–533.10.1007/s10474-017-0721-7
Search in Google Scholar Back to article
[9] DOŠLÁ, Z.—LÍŠKA, P.: Oscillation of third nonlinear neutral differential equations, Appl. Math. Lett. 56 (2016), 42‘48.10.1016/j.aml.2015.12.010
Search in Google Scholar Back to article
[10] DŽURINA, J.—GRACE, S. R.—JADLOVSKÁ, I.: On nonexistence of Knesers solutions of third order delay differential equations, Appl. Math. Lett. 88 (2019), 193–200.10.1016/j.aml.2018.08.016
Search in Google Scholar Back to article
[11] GRAEF, J. R.—TUNC, E.—GRACE, S.R.: Oscillatory and asymptotic behavior of a third order nonlinear neutral differntial equations, Opuscula Math. 37 (2017), 839–852.10.7494/OpMath.2017.37.6.839
Search in Google Scholar Back to article
[12] JIANG, Y. —JIANG, C.—LI, T.: Oscillatory behavior of third order nonlinear neutral delay differential equations, Adv. Difference Equ. 2016 (2016), no. 171, 1–12.10.1186/s13662-016-0902-7
Search in Google Scholar Back to article
[13] KITAMURA, Y.—KUSANO, T.: Oscillation of first order nonlinear differential equations with deviating arguments, Proc. Amer. Math. Soc. 78 (1980), 64–68.10.1090/S0002-9939-1980-0548086-5
Search in Google Scholar Back to article
[14] KOPLATAZE, R. G.—CHANTURIA, T A.: Oscillatory and monotone solutions of first order differential equations with deviating arguments, Differ. Uravn. 18 (1982), no. 8, 1463–1465. (In Russian)
Search in Google Scholar Back to article
[15] ZHANG, S.—WANG, Q.: Oscillation of second-order nonlinear neutral dynamic equations on time scales, Appl. Math. Comput. 216 (2010), 2837–2848.10.1016/j.amc.2010.03.134
Search in Google Scholar Back to article
[16] LI, T.—ROGOVCHENKO, YU. V.: On asymptotic behavior of solutions to higher order sublinear Emden-Fowler delay differential equations, Appl. Math. Lett. 67 (2017), 53–59.10.1016/j.aml.2016.11.007
Search in Google Scholar Back to article
[17] LI, T.—THANDAPANI, E.: Oscillation of solutions to odd order nonlinear neutral functional differential equations, Electron J. Differential Equations 23 (2011), 1–12.10.1155/2011/840569
Search in Google Scholar Back to article
[18] LI, T.—ZHANG, C.: Properties of third order halflinear dynamic equations with an unbounded neutral coefficients, Adv. Difference Equ. 2013 (2013), No. 333, 1–8.10.1186/1687-1847-2013-333
Search in Google Scholar Back to article
[19] PHILOS, CH.G.: On the existence of nonoscillatory solutions tending to zero at ∞ for differential equations with positive delays, Arch. Math. 36 (1981), 168–178.10.1007/BF01223686
Search in Google Scholar Back to article
[20] WONG, J.S.W.: On the generalized Emden-Fowler equation, SIAM Rev. 17 (1975), 339–360.10.1137/1017036
Search in Google Scholar Back to article
[21] TUNC, E.: Oscillatory and asymptotic behavior of third order neutral differential equations with distributed deviating arguments, Electron. J. Differential Equations 2017 (2017), no. 16, 1–12.
Search in Google Scholar Back to article

Articles in this issue

DOI: https://doi.org/10.2478/tmmp-2021-0028 | Journal eISSN: 1338-9750 | Journal ISSN: 1210-3195

Journal RSS Feed

Language: English

Page range: 1 - 14

Submitted on: Mar 17, 2020

Published on: Jan 1, 2022

Published by: Slovak Academy of Sciences, Mathematical Institute

In partnership with: Paradigm Publishing Services

Publication frequency: 1 issue per year

Keywords:

quasi-linear,

neutral differential equation,

Emden-Fowler differential equation,

oscillation

Related subjects:

Mathematics,

General mathematics

© 2022 George E. Chatzarakis, Radhakrishnan Srinivasan, Ethiraju Thandapani, published by Slovak Academy of Sciences, Mathematical Institute
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

Volume 80 (2021): Issue 3 (December 2021)