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2015 | 13 | 1 |
Tytuł artykułu

New interval oscillation criteria for second-order functional differential equations with nonlinear damping

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
This paper concerns the oscillation problem of second-order nonlinear damped ODE with functional terms.We give some new interval oscillation criteria which is not only based on constructing a lower solution of a Riccati type equation but also based on constructing an upper solution for corresponding Riccati type equation. We use a recently developed pointwise comparison principle between those lower and upper solutions to obtain our results. Some illustrative examples are also provided to demonstrate our results.
Słowa kluczowe
Wydawca
Czasopismo
Rocznik
Tom
13
Numer
1
Opis fizyczny
Daty
otrzymano
2014-08-13
zaakceptowano
2015-01-22
online
2015-02-16
Twórcy
  • Department of Mathematics, Sciences & Arts Faculty, Amasya University, Amasya,
    Turkey
Bibliografia
  • [1] M.A. El-Sayed, An oscillation criteria for a forced second-order linear differential equations, Proc. Amer. Math. Soc., 118 (1993),813–817.
  • [2] G.H. Hardy, J.E. Littlewood, G. Polya, Inequalities, second ed., Cambridge University Press, Cambridge, 1988.
  • [3] Y. Huang and F. Meng, Oscillation criteria for forced second-order nonlinear differential equations with damping, Journal ofComputational and Applied Mathematics 224 (2009) 339-345.
  • [4] F. Jiang, F. Meng, New oscillation criteria for a class of second-order nonlinear forced differential equations, J. Math. Anal. Appl.,336 (2007), 1476–1485.
  • [5] Q. Kong, Interval criteria for oscillation of second-order linear ordinary differential equations, J. Math. Anal. Appl., 229 (1999),258–270.
  • [6] W.T. Li, Interval oscillation criteria for second-order quasi-linear nonhomogeneous differential equations with damping, Appl.Math. Comput., 147 (2004), 753–763.
  • [7] Q. Long, Q.R. Wang, New oscillation criteria of second-order nonlinear differential equations, Appl. Math. Comput., 212 (2009),357–365.
  • [8] F. Meng and Y. Huang, Interval oscillation criteria for a forced second-order nonlinear differential equations with damping, AppliedMathematics and Computation 218 (2011) 1857-1861.
  • [9] M. Pasic, Fite-Wintner-Leighton type oscillation criteria for second-order differential equations with nonlinear damping, Abstractand Applied Analysis, Volume 2013 (2013), Article ID 852180, 10 pages.
  • [10] S.P. Rogovchenko and Yu.V. Rogovchenko, Oscillation of second order differential equations with damping, Dynam. Contin.Discrete Impuls.Syst. Ser. A 10 (2003) 447–461.
  • [11] S.P. Rogovchenko, Y.V. Rogovchenko, Oscillation theorems for differential equations with a nonlinear damping term, J. Math. Anal.Appl., 279 (2003), 121–134.
  • [12] N.Shang and H. Qin, Comments on the paper: “Oscillation of second-order nonlinear ODEwith damping” [Applied Mathematicsand Computation 199 (2008) 644–652], Applied Mathematics and Computation 218 (2011) 2979–2980.[WoS]
  • [13] A. Tiryaki, B. Ayanlar, Oscillation theorems for certain nonlinear differential equations of second order, Comput. Math. Appl., 47(2004), 149–159.
  • [14] A. Tiryaki, A. Zafer, Oscillation of second-order nonlinear differential equations with nonlinear damping, Math. Comput. Modelling,39 (2004), 197–208.
  • [15] A. Tiryaki, Y. Ba¸sçı, I. Güleç, Interval criteria for oscillation of second-order functional differential equations, Computers andMathematics with Applications 50 (2005) 1487-1498.
  • [16] YG Sun, C.H. Ou, J.S.W. Wong, Interval oscillation theorems for a second-order linear differential equation, Computers andMathematics with Applications 48 (2004) 1693-1699.
  • [17] YG Sun, J.S.W. Wong, Oscillation criteria for second order forced ordinary differential equations with mixed nonlinearities, J.Math. Anal. Appl. 334 (2007) 549–560.
  • [18] YG Sun, Oscillation of second order functional differential equations with damping, Applied Mathematics and Computation 178(2006) 519–526.
  • [19] Q.R. Wang, X.M. Wu, S.M. Zhu, Oscillation criteria for second-order nonlinear damped differential equations, Comput. Math.Appl., 46 (2003), 1253–1262.
  • [20] J.S.W. Wong, Oscillation criteria for a forced second-order linear differential equations, J. Math. Anal. Appl., 231 (1999), 235–240.
  • [21] L. Xing, Z. Zheng, New oscillation criteria for forced second order halflinear differential equations with damping, Appl. Math.Comput., 198 (2008), 481–486.
  • [22] Q. Yang, Interval oscillation criteria for a forced second-order nonlinear ordinary differential equations with oscillatory potential,Appl. Math. Comput., 135 (2003), 49–64.
  • [23] Q. Yang, R.M. Mathsen, Interval oscillation criteria for second order nonlinear delay differential equations, Rocky MountainJournal of Mathematics, 34 (2004) 1539-1563.[WoS]
  • [24] A. Zhao, Y. Wang, J. Yan, Oscillation criteria for second-order nonlinear differential equations with nonlinear damping, Comput.Math. Appl., 56 (2008), 542–555.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.doi-10_1515_math-2015-0023
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