Oscillation and non-oscillation of neutral difference equations of first order with positive and negative coefficients

• Autorzy: Rath R. , Padhy L. N. , Misra N.
• Języki publikacji: EN

Abstrakty

EN

In this paper necessary and sufficient conditions have been obtained so that every solution of the Neutral Delay Difference Equation (NODE) where different symbols have there usual meaning, oscillates or tends to zero as n → infin for different ranges of {pn}- This paper generalizes some recent work. The results of this paper hold for linear, sublinear or super linear equations and also for homogeneous equations, i.e. when fn equiv 0.

Słowa kluczowe

EN

oscillation; nonoscillation; asymptotic behaviour; neutral difference equation

• Wydawca: Wydawnictwo Politechniki Poznańskiej
• Czasopismo: Fasciculi Mathematici
• Rocznik: 2007
• Tom: Nr 37
• Strony: 57--65
• Opis fizyczny: Bibliogr. 12 poz.

Twórcy

autor

Rath R.

autor

Padhy L. N.

autor

Misra N.

• P.G. Department of Mathematics Khallikote (Autonomous) College Berhampur, Orissa 760 001, India,

Bibliografia

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• [3] GYORI, LADAS G., Oscillation Theory of Delay Differential Equations with Applications, Clarendon Press, Oxford 1991.
• [4] MlCKENS R.E., Difference Equations, Van Nostrand Reinhold Company Inc., New York 1987.
• [5] PARHI N., CHAND S., On forced first order neutral differential equations with positive and negative coefficients, Math. Slovaca, 50(2000), 81-94.
• [6] PARHI N., TRIPATHY A.K., Oscillation criteria for forced nonlinear neutral delay difference equations of first order, Diff. Eqs. and Dyn. Systems, 8(2000), 81-97.
• [7] PARHI N., Oscillation of first order difference equations, Proc. (Math. Sci.) Indian Acad. of Sci., 110(2000), 147-155.
• [8] PARHI N., TRIPATHY A.K., Oscillation of forced non-linear neutral delay difference equations of first order, Czech. Math. J., 53(2003), 83-101.
• [9] PARHI N., TRIPATHY A.K., On asymptotic behaviour and oscillation of forced first order nonlinear neutral difference equations, Fasc. Math., 32(2001), 83-95.
• [10] Yu J.S., WANG Z.C., Asymptotic behaviour and oscillation in neutral delay difference equations, Funk. Ekvac., 37(1994), 241-248.
• [11] Yu J.S., WANG Z.C., Neutral differential equations with positive and negative coefficients, Ada Math. Sinica, 34(1991), 517-523.
• [12] Yu J.S., WANG Z., Some further results on oscillation of neutral differential equations, Bull. Austral. Math. Soc., 416(1992), 149-157.