Oscillatory and asymptotic behavior of solutions of higher order damped nonlinear difference equations
Czechoslovak Mathematical Journal, Tome 49 (1999) no. 1, pp. 149-161 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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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.
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.
Classification : 39A11, 39A12
Keywords: higher order difference equation; oscillation
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Thandapani, E.; Arul, R. Oscillatory and asymptotic behavior of solutions of higher order damped nonlinear difference equations. Czechoslovak Mathematical Journal, Tome 49 (1999) no. 1, pp. 149-161. http://geodesic.mathdoc.fr/item/CMJ_1999_49_1_a14/

[1] R.P. Agarwal: Difference Equations and Inequalities. Marcel Dekker, New York, 1992. | MR | Zbl

[2] R.P. Agarwal: Properties of solutions of higher order nonlinear difference equations I. An. Univ. AI.I. Cuza. Iasi. 31 (1985), 165–172. | MR | Zbl

[3] R.P. Agarwal: Properties of solutions of higher order nonlinear difference equations II. An. Univ. AI.I. Cuza. Iasi 29 (1983), 85–96. | MR | Zbl

[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

[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. | DOI | MR

[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. | DOI | MR

[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

[8] V. Lakshmikantham and D. Trigiante: Theory of Difference Equations: Numerical Methods and Applications. Academic Press, New York, 1988. | MR

[9] J. Popenda: Oscillation and nonoscillation theorems for second order difference equations. J. Math. Anal. Appl. 123 (1987), 34–38. | DOI | MR | Zbl

[10] E. Thandapani: Asymptotic and oscillatory behavior of solutions of nonlinear second order difference equations. Indian. J. Pure. Appl. Math. 24 (1993), 365–372. | MR | Zbl

[11] E. Thandapani: Oscillation theorems for second order damped nonlinear difference equations. Czechoslovak Math. J. 45(120) (1995), 327–335. | MR | Zbl

[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. | DOI | MR

[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

[14] E. Thandapani and P. Sundaram: Oscillation theorems for some even order nonlinear difference equations. J. Nonlinear Diff. Eqn. 4 (1996) (to appear).

[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. | DOI | MR

[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

[17] A. Zafer: On the existence of positive solutions and the oscillation of solutions of higher order difference equations with forcing terms. Preprint. | MR

[18] A. Zafer: Oscillatory and asymptotic behavior of higher order difference equations. Math. Comput. Modelling 21 (1995), 43–50. | DOI | MR | Zbl