Necessary and sufficient conditions for oscillation of solutions of a first order forced nonlinear difference equation with several delays

• Autorzy: Rath R. N. , Padhy L. 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 (NDDE) oscillates or tends to zero as n —> &infin for different ranges of This paper improves and generalizes some recent work [2. 6, 8]. The results of this paper hold for linear, sublinear and superlinear equations and also for homogeneous equations, i.e. when fn ≡ 0.

Słowa kluczowe

EN

oscillation; nonoscillation; asymptotic behaviour; neutral difference equation

PL

równanie różnicowe

• Wydawca: Wydawnictwo Politechniki Poznańskiej
• Czasopismo: Fasciculi Mathematici
• Rocznik: 2005
• Tom: Nr 35
• Strony: 99--113
• Opis fizyczny: Bibliogr. 11 poz.

Twórcy

autor

Rath R. N.

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

autor

Padhy L. N.

• Department of Mathematics K.I.S.T., Bhubaneswar, Orissa, India

Bibliografia

• [1] L.H. Erbe, B.G. Zhang, Oscillation of discrete analogues of delay equations, Diff. Int. Eqs., 2(3)(1989), 300-309.
• [2] D.A. Georgiou, E.A. Grove, G. Ladas, Oscillation of neutral difference equations with variable coefficients. Differential Equations: Stability and Control, Marcel Dekker, (1990), 165-173.
• [3] I. Gyori, G. Ladas, Oscillation Theory of Delay Differential Equations with Applications, Clarendon Press, Oxford, 1991.
• [4] R.E. Mickens, Difference Equations, Van Nostrand Reinhold Company Inc., New York, 1987.
• [5] N. Parhi, R.N. Rath, On oscillation criteria for a forced neutral differential equation, Bull Inst Math. Acad. Sinica, 28(2000), 59-70.
• [6] N. Parhi, A.K. Tripathy, Oscillation criteria for forced nonlinear neutral delay difference equations of first order, Differential Equations and Dynamical systems, 8(2000), 81-97.
• [7] N. Parhi, R.N. Rath, Oscillation criteria for first order neutral differential equations with variable coefficient, J. Math. Anal. Appl., 256(2001), 525-541.
• [8] N. Parhi, Behaviour of solutions of delay-difference equations of first order, Indian J. Pure. Appl. Math., 33(2002), 31-43.
• [9] N. Parhi, A.K. Tripathy, Oscillation of forced nonlinear neutral delay-difference equations of first order, Czech. Math. J., (in press).
• [10] J.S. Yu, Z.C. Wang, Asymptotic behaviour and oscillation in neutral delay difference equations. Funk. Ekvec., 37(1994), 241-248.
• [11] J.S. Yu, B.G. Zhang, Z.C. Wang, Oscillation of delay difference equations, Appl. Anal, 53(1994), 117-124.