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## Open Mathematics

2004 | 2 | 1 | 57-66
Tytuł artykułu

### Oscillation results for second order nonlinear differential equations

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EN
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EN
In this paper, the authors present some new results for the oscillation of the second order nonlinear neutral differential equations of the form $$\left( {r\left( t \right)\psi \left( {x\left( t \right)} \right)\left[ {x\left( t \right) + p\left( t \right)x\left( {\tau \left( t \right)} \right)} \right]^\prime } \right)^\prime + q\left( t \right)f\left( {x\left[ {\sigma \left( t \right)} \right]} \right) = 0$$ . Easily verifiable criteria are obtained that are also new for differential equations without neutral term i.e. for p(t)≡0.
Słowa kluczowe
EN
Wydawca
Czasopismo
Rocznik
Tom
Numer
Strony
57-66
Opis fizyczny
Daty
wydano
2004-03-01
online
2004-03-01
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autor
autor
Bibliografia
• [1] D.D. Bainov and D.P. Mishev: Oscillation Theory for Neutral Differential Equations with Delay, Adam Hilger, Bristol, Philadelphia, New York, 1991.
• [2] M. Budincevic: “Oscillation of second order neutral nonlinear differential equations”, Novi Sad J. Math., Vol. 27, (1997), pp. 49–56.
• [3] T.A. Chanturija and I.T. Kiguradze: Asymptotic properties of solutions of nonautonomous ordinary differential equations. Nauka, Moscow, 1991. (Russian)
• [4] L.H. Erbe, Q. Kong, B.G. Zhang: Oscillation Theory for Functional Differential Equations, Adam Hilger, New York, Basel, Hong Kong, 1991.
• [5] L.H. Erbe and Q. Kong: “Oscillation résults for second order neutral differential equations”, Funk. Ekvacioj, Vol. 35, (1992), pp. 545–557.
• [6] Q. Chuanxi and G. Ladas: “Oscillations of higher order neutral differential equations with variable coefficients”, Math. Nachr., Vol. 150, (1991), pp. 15–24.
• [7] S.R. Grace and B.S. Lalli: “Oscillation and asymptotic behavior of certain second order neutral differential equations”, Radovi Mat., Vol. 5, (1989), pp. 121–126.
• [8] M.K. Grammatikopoulos, G. Ladas and A. Meimaridou: “Oscillation and asymptotic behavior of higher order neutral equations with variable coefficients”, Chin. Ann. of Math., Vol. 9B, (1988), pp. 322–338.
• [9] K. Gopalsamy, B.S. Lalli and B.G. Zhang: “Oscillation of odd order neutral differential equations”, Czech. Math. J., Vol. 42, (1992), pp. 313–323.
• [10] I. Győri and G. Ladas: Theory of Delay Differential Equations with Applications, Clarendon Press, Oxford, (1991).
• [11] J. Hale: Theory of functional differential equations, Springer-Verlag, New York, 1977.
• [12] N. Parhi and P.K. Mohanty: “Oscillation of neutral differential equations of higher order”, Bull. Inst. Math. Sinica, Vol. 24, (1996), pp. 139–150.
• [13] M. Ružičková and E. Špániková: “Comparison theorems for differential equations of neutral type”, Fasc. Math., Vol. 128, (1998), pp. 141–148.
• [14] P. Wang, Y. Yu: “Oscillation of second order order neutral equations with deviating argument”, Math. J. Toyama Univ., Vol. 21, (1998), pp. 55–66.
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Bibliografia
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