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2019 | Vol. 39, no. 1 | 39--47
Tytuł artykułu

Oscillatory behavior of even-order nonlinear differential equations with a sublinear neutral term

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
The authors present a new technique for the linearization of even-order nonlinear differential equations with a sublinear neutral term. They establish some new oscillation criteria via comparison with higher-order linear delay differential inequalities as well as with first-order linear delay differential equations whose oscillatory characters are known. Examples are provided to illustrate the theorems.
Wydawca

Rocznik
Strony
39--47
Opis fizyczny
Bibliogr. 20 poz.
Twórcy
  • University of Tennessee at Chattanooga Department of Mathematics Chattanooga, TN 37403, USA, John-Graef@utc.edu
  • Cairo University Department of Engineering Mathematics Faculty of Engineering, Orman, Giza 12221, Egypt, saidgrace@yahoo. com
autor
  • Gaziosmanpasa University Department of Mathematics Faculty of Arts and Sciences, 60240, Tokat, Turkey, ercantunc72@yahoo.com
Bibliografia
  • [1] R.P. Agarwal, S.R. Grace, The oscillation of higher-order differential equations with deviating arguments, Comput. Math. Appl. 38 (1999), 185-199.
  • [2] R.P. Agarwal, S.R. Grace, Oscillation theorems for certain functional differential equations of higher order, Math. Comput. Model. 39 (2004), 1185-1194.
  • [3] R.P. Agarwal, M. Bohner, T. Li, C. Zhang, Oscillation of second-order differential equations with a sublinear neutral term, Carpathian J. Math. 30 (2014), 1-6.
  • [4] R.P. Agarwal, S.R. Grace, I.T. Kiguradze, D. O'Regan, Oscillation of functional differential equations, Math. Comput. Model. 41 (2005), 417-461.
  • [5] R.P. Agarwal, S.R. Grace, D. O'Regan, Oscillation criteria for certain nth order differential equations with deviating arguments, J. Math. Anal. Appl. 262 (2001), 601-622.
  • [6] R.P. Agarwal, S.R. Grace, D. O'Regan, Oscillation of certain fourth-order functional differential equations, Ukrainian Math. J. 59 (2007), 315-342.
  • [7] R.P. Agarwal, S.R. Grace, D. O'Regan, Oscillation Theory for Difference and Functional Differential Equations, Kluwer Academic Publishers, Dordrecht, 2000.
  • [8] R.P. Agarwal, S.R. Grace, P.J.Y. Wong, On the bounded oscillation of certain fourth order functional differential equations, Nonlinear Dyn. Syst. Theory 5 (2005), 215-227.
  • [9] B. Baculikova, J. Dżurina, Oscillation theorems for second-order nonlinear neutral differential equations, Comput. Math. Appl. 62 (2011), 4472-4478.
  • [10] S.R. Grace, Oscillation theorems for nth-order differential equations with deviating arguments, J. Math. Anal. Appl. 101 (1984), 268-296.
  • [11] S.R. Grace, B.S. Lalli, On oscillation and nonoscillation of general functional differential equations, J. Math. Anal. Appl. 109 (1985), 522-533.
  • [12] S.R. Grace, B.S. Lalli, A comparison theorem for general nonlinear ordinary differential equations, J. Math. Anal. Appl. 120 (1986), 39-43.
  • [13] S.R. Grace, R.P. Agarwal, M. Bohner, D. O'Regan, Oscillation of second-order strongly superlinear and strongly sublinear dynamic equations, Commun. Nonlinear Sci. Numer. Simul. 14 (2009), 3463-3471.
  • [14] I. Gyóri, G. Ladas, Oscillation Theory of Delay Differential Equations with Applications, Clarendon Press, Oxford, 1991.
  • [15] G.H. Hardy, I.E. Littlewood, G. Polya, Inequalities, Reprint ol the 1952 edition, Cambridge University Press, Cambridge, 1988.
  • [16] I.T. Kiguradze, On the oscillatory character of solutions of the equation dmu/dtm + a{t)\u\nsgnu = 0, Mat. Sb. (N.S.) 65 (1964), 172-187.
  • [17] T. Li, Y.V. Rogovchenko, Oscillation criteria for even-order neutral differential equations, Appl. Math. Lett. 61 (2016), 35-41.
  • [18] Ch.G. Philos, On the existence of nonosdilatory solutions tending to zero at oo for differential equations with positive delays, Arch. Math. (Basel) 36 (1981), 168-178.
  • [19] Ch.G. Philos, A new criterion for the oscillatory and asymptotic behavior of delay differential equations, Bull. Acad. Pol. Sci. Ser. Sci. Mat. 30 (1981), 61-64.
  • [20] Q. Zhang, J. Yan, L. Gao, Oscillation behavior of even-order nonlinear neutral differential equations with variable coefficients, Comput. Math. Appl. 59 (2010), 426-430.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.baztech-1d5aa751-13e5-41ee-bfeb-9c3049d97c1e
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