1. bookVolumen 79 (2021): Edición 2 (December 2021)
Detalles de la revista
License
Formato
Revista
eISSN
1338-9750
Primera edición
12 Nov 2012
Calendario de la edición
3 veces al año
Idiomas
Inglés
access type Acceso abierto

Oscillatory Behaviour of Second-Order Nonlinear Differential Equations with Mixed Neutral Terms

Publicado en línea: 01 Jan 2022
Volumen & Edición: Volumen 79 (2021) - Edición 2 (December 2021)
Páginas: 119 - 134
Recibido: 11 Sep 2020
Detalles de la revista
License
Formato
Revista
eISSN
1338-9750
Primera edición
12 Nov 2012
Calendario de la edición
3 veces al año
Idiomas
Inglés
Abstract

The authors examine the oscillation of second-order nonlinear differential equations with mixed nonlinear neutral terms. They present new oscillation criteria that improve, extend, and simplify existing ones in the literature. The results are illustrated by some examples.

Keywords

[1] AGARWAL, R.P.— BOHNER, M.— LI, T.— ZHANG, C.: Oscillation of second-order differential equations with a sublinear neutral term, Carpathian J. Math. 30 (2014), 1–6.10.37193/CJM.2014.01.01 Search in Google Scholar

[2] AGARWAL, R.P.— GRACE, S.R.—O’REGAN, D.: Oscillation Theory for Difference and Functional Differential Equations. Kluwer Academic Publishers, Dordrecht, 2010. Search in Google Scholar

[3] AGARWAL, R.P.—GRACE, S.R.—O’REGAN, D.: Oscillation Theory for Second Order Linear, Half-Linear, Superlinear and Sublinear Dynamic Equations. Kluwer Academic Publishers, Dordrecht, 2010. Search in Google Scholar

[4] BOHNER, M.—GRACE, S.R.—JADLOVSKÁ, I.: Oscillation criteria for second-order neutral delay differential equations, Electron. J. Qual. Theory Differ. Equ. 2017 (2017), no. 60, 1–12. Search in Google Scholar

[5] GRACE, S. R.: Oscillatory behavior of second-order nonlinear differential equations with a nonpositive neutral term, Mediterr. J. Math. 14 (2017), Paper no. 229, 1–12. Search in Google Scholar

[6] GRACE, S. R.—GRAEF, J. R.: Oscillatory behavior of second order nonlinear differential equations with a sublinear neutral term, Math. Model. Anal. 23 (2018), 217–226.10.3846/mma.2018.014 Search in Google Scholar

[7] GRAEF, J. R.—GRACE, S. R.—TUNÇ, E.: Oscillatory behavior of even-order nonlinear differential equations with a sublinear neutral term, Opuscula Math. 39 (2019), 39–47.10.7494/OpMath.2019.39.1.39 Search in Google Scholar

[8] GRAEF, J. R.—GRACE, S.R.—TUNÇ, E.: Oscillation of even-order nonlinear differential equations with sublinear and superlinear neutral terms, Publ. Math. Debrecen (to appear). Search in Google Scholar

[9] GRAEF, J. R.—GRAMMATIKOPOULOS, M. K.—SPIKES, P.W.: On the asymptotic behavior of solutions of a second order nonlinear neutral delay differential equation, J. Math. Anal. Appl. 156 (1991), 23–39.10.1016/0022-247X(91)90379-E Search in Google Scholar

[10] GRAEF, J. R.—SPIKES, P. W.: On the oscillation of an nth-order nonlinear neutral delay differential equation, J. Comput. Appl. Math. 41 (1992), 35–40.10.1016/0377-0427(92)90235-P Search in Google Scholar

[11] HALE, J. K.: Theory of Functional Differential Equations. Springer, New York, 1977.10.1007/978-1-4612-9892-2 Search in Google Scholar

[12] HARDY, G. H.—LITTLEWOOD, I.E.—POLYA, G.: Inequalities. Reprint of the 1952 edition, Cambridge University Press, Cambridge, 1988. Search in Google Scholar

[13] KOPLATADZE, R.G.—CHANTURIYA, T. A.: Oscillating and monotone solutions of first-order differential equations with deviating argument, Differ. Uravn. 18 (1982), 1463–1465. (In Russian) Search in Google Scholar

[14] LADAS, G.—STAVROULAKIS, I. P.: Oscillation caused by several retarded and advanced arguments, J. Differ. Equations 44 (1982), 134–152.10.1016/0022-0396(82)90029-8 Search in Google Scholar

[15] LI, T.—ROGOVCHENKO, YU. V.: Oscillation of second-order neutral differential equations, Math. Nachr. 288 (2015), 1150–1162.10.1002/mana.201300029 Search in Google Scholar

[16] LI, T.—ROGOVCHENKO, YU. V.—ZHANG, C.: Oscillation results for second-order nonlinear neutral differential equations, Adv. Differ. Equ. 2013 (2013), Paper no. 336, 13 pp. Search in Google Scholar

[17] PHILOS, CH. G.: On the existence of nonoscillatory solutions tending to zero at ∞ for differential equations with positive delays, Arch. Math. (Basel) 36 (1981), 168–178.10.1007/BF01223686 Search in Google Scholar

[18] QIN, H.—SHANG, N.—LU, Y.: A note on oscillation criteria of second order nonlinear neutral delay differential equations, Comput. Math. Appl. 56 (2008), 2987–2992.10.1016/j.camwa.2008.09.004 Search in Google Scholar

[19] TAMILVANAN, S.—THANDAPANI, E.—DŽURINA, J.: Oscillation of second order nonlinear differential equation with sub-linear neutral term, Differ. Equ. Appl. 9 (2017), 29–35. Search in Google Scholar

[20] XU, R.—MENG, F.: Some new oscillation criteria for second order quasi-linear neutral delay differential equations, Appl. Math. Comput. 182 (2006), 797–803.10.1016/j.amc.2006.04.042 Search in Google Scholar

[21] WONG, J. S. W.: Necessary and sufficient conditions for oscillation of second order neutral differential equations, J. Math. Anal. Appl. 252 (2000), 342–352.10.1006/jmaa.2000.7063 Search in Google Scholar

[22] WU, H.—ERBE, L.—PETERSON, A.: Oscillation of solution to second-order half-linear delay dynamic equations on time scales, Electron. J. Differential Equations 2016 (2016), no. 71, 1–15. Search in Google Scholar

Artículos recomendados de Trend MD

Planifique su conferencia remota con Sciendo