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Asymptotic properties of nonoscillatory solutions of higher order neutral difference equations

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In this paper we study asymptotic behavior of solutions of a higher order neutral difference equation of the form Δm(xn + pnxn-τ) + f(n, xσ(n)) = hn. We present conditions under which all nonoscillatory solutions of the above equation have the property xn = cnm-1 + o(nm-1) for some c ∈ R.
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507--514
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Bibliogr. 14 poz.
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Bibliografia
  • [1] A. Drozdowicz, M. Migda, Asymptotic behavior of solutions of the mth-order nonhomogeneous difference equations, J. Comput. Appl. Math. 81 (1997) 1, 75-81.
  • [2] A. Gleska, J. Werbowski, Comparison theorems for the asymptotic behavior of solutions of nonlinear difference equations, J. Math. Anal. Appl. 226 (1998) 2, 456-465.
  • [3] W.T. Li, S.S. Cheng, Asymptotic trichotomy for positive solutions of a class of odd order nonlinear neutral difference equations, Computers Math. Applic. 35 (1998), 101-108.
  • [4] J.R. Graef, A. Miciano, P. Spikes, P. Sundaram, E. Thandapani, Oscilatory and asymptotic behavior of solutions of nonlinear neutral-type difference equations, J. Austral. Math. Soc. 38 (1996), 163-171.
  • [5] M. Migda, J. Migda, On the asymptotic behavior of solutions of higher order nonlinear difference equations, Nonlinear Anal. 47 (2001) 7, 4687-4695.
  • [6] M. Migda, J. Migda, Asymptotic properties of solutions of second-order neutral difference equations, Nonlinear Anal. 63 (2005), e789-e799.514
  • [7] M. Migda, On unstable neutral difference equations of higher order, Indian J. Pure Appl. Math. 36(10) (2005), 557-567.
  • [8] N. Parhi, A.K. Tripathy, Oscillation of a class of nonlinear neutral difference equations of higher order, J. Math. Anal. Appl. 284 (2003), 756-774.
  • [9] B. Szmanda, Note on the behaviour of solutions of difference equations of arbitrary order, Univ. Beograd. Publ. Elektrotehn. Fak. Ser. Mat. 8 (1997), 52-59.
  • [10] E. Thandapani, P. Sundaram, J.R. Graef, A. Miciano, P. Spikes, Classification of nonoscillatory solutions of higher order neutral type difference equations, Arch. Math. (Brno) 31 (1995), 263-277.
  • [11] E. Thandapani, P. Sundaram, J.R. Graef, P.W. Spikes, Asymptotic behaviour and oscillation of solutions of neutral delay difference equations of arbitrary order, Math. Slovaca 47 (1997), 539-551.
  • [12] A. Zafer, Y. Yalin, Y.S. Yilmaz, Positive solutions and oscillation of higher order neutral difference equations, Arch. Math. (Brno) 36 (2000), 623-636.
  • [13] A. Zafer, Oscillatory and asymptotic behavior of higher order difference equations, Math. Comput. Modelling 21, 4(1995), 43-50.
  • [14] Y. Zhou, B.G. Zhang, Existence of nonoscillatory solutions of higher-order neutral delay difference equations with variable coefficients, Computers Math. Applic. 45 (2003), 991-1000.
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Bibliografia
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bwmeta1.element.baztech-article-AGH4-0007-0101
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