Oscillation and non-oscillation criteria for a neutral delay difference equation of first order

• Autorzy: Rath R. , Rath S. K.
• Języki publikacji: EN

Abstrakty

EN

In this paper, necessary and sufficient condition are obtained so that every bounded solution of Δ(y_n - y_{n-k) + qn}G(y_σ(n)) = 0 is oscillatory, under a condition weaker than ...[wzór]

Słowa kluczowe

EN

oscillatory solution; nonoscillatory solution; asymptotic behaviour; difference equation

PL

zachowanie asymptotyczne; równanie różniczkowe

• Wydawca: Wydawnictwo Politechniki Poznańskiej
• Czasopismo: Fasciculi Mathematici
• Rocznik: 2009
• Tom: Nr 42
• Strony: 109--120
• Opis fizyczny: Bibliogr. 20 poz.

Twórcy

autor

Rath R.

autor

Rath S. K.

• Department of Mathematics V.S.S. University of Technology Burla, Sambalpur, 768018, Orissa, India,

Bibliografia

• [1] Agarwal R.P., Difference equations and inequalities, Marcel Dekker, New York 2000.
• [2] Cheng S.S., Patula W.T., An existence theorem for a non linear difference equation, Nonlinear Analysis, 20(1993), 193-203.
• [3] Das P., Misra N., A necessary and sufficient condition for the solution of a functional differential equation to be oscillatory or tend to zero, J. Math. Anal. Appl., 204(1997), 78-87.
• [4] Elaydi S.N., An introduction to difference equations, Springer Verlag, New York 1996.
• [5] Erbe L.H., Kong Q.K., Zhang B.G., Oscillation theory for functional differential equations, Marcel Dekker, New York 1995.
• [6] Gyori I., Ladas G., Oscillation theory of delay differential equations with applications, Clarendon Press, Oxford 1991.
• [7] Karpuz B., Rath R.N., Rath S.K., On Oscillation and asymptotic behavior of a higher order functional difference equation of neutral type, Communicated.
• [8] Kelley W.G., Peterson A.C., Difference equations: An introduction with applications, Academic Press, New York 1991.
• [9] Li Q., Liang H., Dong W., Zhang Z., Existence of non-oscillatory solutions to higher-order mixed difference equations, Electronic J. Differential Equations, 9(2007), 1-7.
• [10] Lalli B.S., etal, On the oscillation of solutions and existence of positive solutions of neutral difference equations, J. Math. Anal. Appl., 158(1991), 213-233.
• [11] Mickens R.E., Difference equations, Van Nostrand Reinhold Company Inc., New York 1987.
• [12] Parhi N., Tripathy A.K., Oscillation criteria for forced non-linear neutral delay difference equations of first order, Diff. Eqs. and Dyn. Systems, 8(2000), 81-97.
• [13] Parhi N., Tripathy A.K., On asymptotic behaviour and oscillation of forced first order nonlinear neutral difference equations, Fasc. Math., 32(2001), 83-95.
• [14] Parhi N., Rath R.N., On oscillation and asymptotic behaviour of solutions of forced first order neutral differential equations, Proceedings of Indian Acad. Sci. Math. Sci., 111(2001), 337-350.
• [15] Parhi N., Tripathy A.K., Oscillation of forced nonlinear neutral delay difference equations of first order, Czech. Math. J., 53(2003), 83-101.
• [16] Parhi N., Tripathy A.K., Oscillation of a class of neutral difference equations of first order, J. of Diff. Equat. and Appl., 9(10)(2003), 933-946.
• [17] Rath R.N., Misra N., Necessary and sufficient conditions for oscillatory behaviour of solutions of a forced nonlinear neutral equation of first order with positive and negative coefficients, Math. Slovaca, 54(2004), 255-266.
• [18] Rath R.N., Padhy L.N., Necessary and sufficient conditions for oscillation of solutions of a first order forced nonlinear difference equation with several delays, Fasc. Math., 35(2005), 99-113.
• [19] Rath R.N., Padhy L.N., Misra N., Oscillation and non-oscillation of neutral difference equations of first order with positive and negative coefficients, Fasc. Math., 37(2007), 57-65.
• [20] Thandapani E., Arul R., Roja P.S., Oscillatory and asymptotic behavior of solutions of non-homogeneous neutral difference equations, Studies of the University of Zilina Mathematical Series, 15(2002), 67-82.