Abstract
This paper is concerned with a class of neutral difference equations of second order with positive and negative coefficients of the forms $$ \Delta ^2 (x_n \pm c_n x_{n - \tau } ) + p_n x_{n - \delta } - q_n x_{n - \sigma } = 0 $$ where τ, δ and σ are nonnegative integers and {p n}, {q n} and {c n} are nonnegative real sequences. Sufficient conditions for oscillation of the equations are obtained.
[1] LADAS, G.— QIAN, C.: Oscillations in differential equations with positive and negative coefficients, Canad. Math. Bull. 33 (1990), 442–450. 10.4153/CMB-1990-072-xSearch in Google Scholar
[2] LADAS, G.— QIAN, C.: Oscillatory behaviour of difference equations with positive and negative coefficients, Matematiche (Catania) 44 (1989), 293–309. Search in Google Scholar
[3] GRACE, S.R.— HAMEDANI, G.G.: On the oscillation of certain neutral difference equations, Math. Bohem. 125 (2000), 307–321. 10.21136/MB.2000.126132Search in Google Scholar
[4] GYORI, I.— LADAS, G.: Oscillation Theory of Delay Differential Equations, Clarendon Press, Oxford, 1991. Search in Google Scholar
[5] LADAS, G.: Oscillation of difference equations with positive and negative coefficients, Rocky Mountain J. Math. 20 (1990), 1051–1061. http://dx.doi.org/10.1216/rmjm/118107306210.1216/rmjm/1181073062Search in Google Scholar
[6] JELENA, V.— MANOJLOVIC, J.— SHOUKAKU, Y.— TANIGAWA, T.— YOSHIDA, N.: Oscillation criteria for second order differential equations with positive and negative coefficients, Appl. Math. Comput. 181 (2006), 853–863. http://dx.doi.org/10.1016/j.amc.2006.02.01510.1016/j.amc.2006.02.015Search in Google Scholar
[7] PADHI, S.: Oscillation and asymptotic behaviour of solutions of second order neutral differential equations with positive and negative coefficients, Fasc. Math. 38 (2007), 105–114. Search in Google Scholar
[8] PARHI, N.— CHAND, S.: Oscillations of second order neutral delay differential equations with positive and negative coefficients, J. Indian Math. Soc. (N.S.) 66 (1999), 227–235. Search in Google Scholar
[9] PARHI, N.— TRIPATHY, A. K.: Oscillation of a class of nonlinear neutral difference equations of higher order, J. Math. Anal. Appl. 284 (2003), 756–774. http://dx.doi.org/10.1016/S0022-247X(03)00298-110.1016/S0022-247X(03)00298-1Search in Google Scholar
[10] TANG, X. H.— CHENG, S. S.: Positive solutions of a neutral difference equations with positive and negative coefficients, Georgian Math. J. 11 (2004), 177–186. 10.1515/GMJ.2004.177Search in Google Scholar
[11] TANG, X.H.— YU, J.S.— PENG, D.H.: Oscillation and nonoscillation of neutral difference equations with positive and negative coefficients, Comput. Math. Appl. 39 (2000), 169–181. http://dx.doi.org/10.1016/S0898-1221(00)00073-010.1016/S0898-1221(00)00073-0Search in Google Scholar
[12] THANDAPANI, E.— LIU, Z.— ARUL, R.— RAJA, P. S.: Oscillation and asymptotic behaviour of second order difference equations with a nonlinear neutral term, Appl. Math. E-Notes 4 (2004), 59–67. Search in Google Scholar
[13] TIAN, C.— CHENG, S. S.: Oscillation criteria for delay neutral difference equations with positive and negative coefficients, Bol. Soc. Parana. Mat. (2) 21 (2003), 1–12. Search in Google Scholar
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