1. bookVolumen 80 (2021): Heft 3 (December 2021)
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License
Format
Zeitschrift
eISSN
1338-9750
Erstveröffentlichung
12 Nov 2012
Erscheinungsweise
3 Hefte pro Jahr
Sprachen
Englisch
access type Uneingeschränkter Zugang

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

Online veröffentlicht: 01 Jan 2022
Volumen & Heft: Volumen 80 (2021) - Heft 3 (December 2021)
Seitenbereich: 1 - 14
Eingereicht: 17 Mar 2020
Zeitschriftendaten
License
Format
Zeitschrift
eISSN
1338-9750
Erstveröffentlichung
12 Nov 2012
Erscheinungsweise
3 Hefte pro Jahr
Sprachen
Englisch
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)yλ(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.

[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

[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

[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

[4] TANG, X. H.: Oscillation for first order superlinear delay differential equations, J. London Math. Soc. 65 (2002), no. 1, 115–122. Search in Google Scholar

[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

[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

[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

[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

[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

[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

[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

[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. Search in Google Scholar

[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

[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

[15] ZHANG, S.—WANG, Q.: Oscillation of second-order nonlinear neutral dynamic equations on time scales, Appl. Math. Comput. 216 (2010), 2837–2848. Search in Google Scholar

[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

[17] LI, T.—THANDAPANI, E.: Oscillation of solutions to odd order nonlinear neutral functional differential equations, Electron J. Differential Equations 23 (2011), 1–12. Search in Google Scholar

[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. Search in Google Scholar

[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

[20] WONG, J.S.W.: On the generalized Emden-Fowler equation, SIAM Rev. 17 (1975), 339–360.10.1137/1017036 Search in Google Scholar

[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

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