# Article

 Title: Oscillatory and asymptotic behavior of solutions of higher order damped nonlinear difference equations (English) Author: Thandapani, E. Author: Arul, R. Language: English Journal: Czechoslovak Mathematical Journal ISSN: 0011-4642 (print) ISSN: 1572-9141 (online) Volume: 49 Issue: 1 Year: 1999 Pages: 149-161 Summary lang: English . Category: math . Summary: The asymptotic and oscillatory behavior of solutions of mth order damped nonlinear difference equation of the form $\Delta (a_n \Delta ^{m-1} y_n) + p_n \Delta ^{m-1} y_n + q_n f(y_{\sigma (n+m-1)}) = 0$ where $m$ is even, is studied. Examples are included to illustrate the results. (English) Keyword: higher order difference equation Keyword: oscillation MSC: 39A11 MSC: 39A12 idZBL: Zbl 0954.39002 idMR: MR1676817 . Date available: 2009-09-24T10:20:58Z Last updated: 2020-07-03 Stable URL: http://hdl.handle.net/10338.dmlcz/127475 . Reference: [1] R.P. Agarwal: Difference Equations and Inequalities.Marcel Dekker, New York, 1992. Zbl 0925.39001, MR 1155840 Reference: [2] R.P. Agarwal: Properties of solutions of higher order nonlinear difference equations I.An. Univ. AI.I. Cuza. Iasi. 31 (1985), 165–172. Zbl 0599.39001, MR 0858057 Reference: [3] R.P. Agarwal: Properties of solutions of higher order nonlinear difference equations II.An. Univ. AI.I. Cuza. Iasi 29 (1983), 85–96. Zbl 0599.39002, MR 0739573 Reference: [4] S.R. Grace and B.S. Lalli: Oscillation theorems for $n$-th order delay differential equations.J. Math. Anal. Appl. 91 (1983), 342–366. MR 0690876 Reference: [5] S.R. Grace and B.S. Lalli: Oscillation theorems for damped differential equations of even order with deviating arguments.SIAM. J. Math. Anal. 15 (1984), 308–316. MR 0731869, 10.1137/0515024 Reference: [6] J.W. Hooker and W.T. Patula: A second order nonlinear difference equation: Oscillation and asymptotic behavior.J. Math. Anal. Appl. 91 (1983), 9–29. MR 0688528, 10.1016/0022-247X(83)90088-4 Reference: [7] M.R.S. Kulenovic and M. Budincevic: Asymptotic analysis of nonlinear second order difference equations.Anal. Sti. Univ. Iasi. 30 (1984), 39–52. MR 0800139 Reference: [8] V. Lakshmikantham and D. Trigiante: Theory of Difference Equations: Numerical Methods and Applications.Academic Press, New York, 1988. MR 0939611 Reference: [9] J. Popenda: Oscillation and nonoscillation theorems for second order difference equations.J. Math. Anal. Appl. 123 (1987), 34–38. Zbl 0612.39002, MR 0881528, 10.1016/0022-247X(87)90291-5 Reference: [10] E. Thandapani: Asymptotic and oscillatory behavior of solutions of nonlinear second order difference equations.Indian. J. Pure. Appl. Math. 24 (1993), 365–372. Zbl 0784.39003, MR 1229844 Reference: [11] E. Thandapani: Oscillation theorems for second order damped nonlinear difference equations.Czechoslovak Math. J. 45(120) (1995), 327–335. Zbl 0838.39003, MR 1331469 Reference: [12] E. Thandapani, P. Sundaram and B.S. Lalli: Oscillation theorems for higher order nonlinear delay difference equations.Computers Math. Applic. 32 (1996), 111–117. MR 1398552, 10.1016/0898-1221(96)00116-2 Reference: [13] E. Thandapani, P. Sundaram, J.R. Graef, A. Miciano and P.W. Spikes: Classification of nonoscillatory solutions of higher order neutral type difference equations.Arch. Math. (Brno) 31 (1995), 263–277. MR 1390585 Reference: [14] E. Thandapani and P. Sundaram: Oscillation theorems for some even order nonlinear difference equations.J. Nonlinear Diff. Eqn. 4 (1996) (to appear). Reference: [15] P.J.Y. Wong and R.P. Agarwal: Oscillation theorems and existence of positive monotone solutions for second order non linear difference equations.Math. Comp. Modelling 21 (1995), 63–84. MR 1316120, 10.1016/0895-7177(94)00215-A Reference: [16] P.J.Y. Wong and R.P. Agarwal: The oscillation of an $m$-th order perturbed nonlinear difference equation.Arch. Math. (Brno) 32 (1996), 13–27. MR 1399838 Reference: [17] A. Zafer: On the existence of positive solutions and the oscillation of solutions of higher order difference equations with forcing terms.Preprint. MR 1666123 Reference: [18] A. Zafer: Oscillatory and asymptotic behavior of higher order difference equations.Math. Comput. Modelling 21 (1995), 43–50. Zbl 0820.39001, MR 1317929, 10.1016/0895-7177(95)00005-M .

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