Neutral differential equations are one of the most important extensions of classical ordinary differential equations and aim to give a better explanation for modeling phenomena where ordinary differential equations are insufficient. Naturally, all the questions studied in the scope of ordinary differential equations attracted the attention also for neutral differential equations. In this paper we study the oscillatory properties of second order half-linear neutral differential equations. We present oscillation criteria derived using a new approach. This approach allows us to reduce common restrictions on the deviations in arguments which are present in the currently known results of this type.
Bohner, M.—Grace, S. R.—Jadlovská, I.: Oscillation criteria for second-order neutral delay differential equations Electron. J. Qual. Theory Differ. Equ. 60 (2017), 1–12.
Džurina, J.—Grace, S. R.—Jadlovská, I.— Li, T.: Oscillation criteria for second-order Emden-Fowler delay differential equations with a sublinear neutral term, Math. Nachr. (2019), in press.
Fišnarová, S.: Oscillation criteria for neutral half-linear differential equations without commutativity in deviating arguments, Electron. J. Qual. Theory Differ. Equ. 51 (2016), 1–10.
Fišnarová, S.—Mařík, R.: On eventually positive solutions of quasilinear second order neutral differential equations, Abstr. Appl. Anal. 2014, Art. ID 818732.
Fišnarová, S.—Mařík, R.: Oscillation of neutral second order half-linear differential equations without commutativity in deviating arguments, Math. Slovaca 67(3) (2017), 701–718.
Grace, S. R.—Džurina, J.—Jadlovská, I.—Li, T.: An improved approach for studying oscillation of second-order neutral delay differential equations, J. Inequal. Appl. 2018 (2018), 1–13.
Hale, J. K.—Verdyun Lunel, S. M.: Introduction to Functional Differential Equations, Springer-Verlag, 1993.
Hasanbulli, M.—Rogovchenko, Y.: Oscillation criteria for second order nonlinear neutral differential equations, Appl. Math. Comp. 215 (2010), 4392–4399.
Koplatadze, R. G.—Chanturiya, T. A.: Oscillating and monotone solutions of first-order differential equations with deviating argument, Differentsial’nye Uravneniya 18(8) (1982), 1463–1465 (in Russian).
Li, T.—Baculíková, B.—Džurina, J.: Oscillation results for second-order neutral differential equations of mixed type, Tatra Mt. Math. Publ. 48 (2011), 101–116.
Li, T.—Rogovchenko, Yu. V.: Oscillation theorems for second-order neutral delay differential equations, Abstr. Appl. Anal. (2014), Art. ID 594190.