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Qualitative properties of solutions of higher order difference equations with deviating arguments

  • * Corresponding author: Alina Gleska

    * Corresponding author: Alina Gleska 
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  • In the paper the general higher order difference equation

    $(-1)^z Δ^m x(n)=f(n, x(σ_1(n)),x(σ_2(n)),..., x(σ_k(n)))$

    with several deviating arguments is considered. According to the kind of the deviations $σ_i$ sufficient conditions for the equation to have property A and B are established.

    Mathematics Subject Classification: Primary: 39A10.

    Citation:

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  •   R. P. Agarwal, M. Bohner, S. R. Grace and D. O'Regan, Discrete Oscillation Theory Hindawi Publishing Corporation, New York, 2005. doi: 10.1155/9789775945198.
      R. P. Agarwal, Difference Equations and Inequalities. Theory, Methods, and Applications Second Edition, Revised and Expanded, Marcel Dekker, New York, 2000.
      J. Baštinec, L. Berezansky, J. Diblík and Z. šmarda, A final result on the oscillation of solutions of the linear discrete delayed equation $Δ x(n)=-p(n)x(n-k)$ with a positive coefficient Abstract and Applied Analysis 2011 (2011), Art. ID 586328, 28 pp. doi: 10.1155/2011/586328.
      G. E. Chatzarakis , R. Koplatadze  and  I. P. Stavroulakis , Oscillation criteria of first order linear difference equations with delay argument, Nonlinear Anal., 68 (2008) , 994-1005.  doi: 10.1016/j.na.2006.11.055.
      G. E. Chatzarakis , M. Lafci  and  I. P. Stavroulakis , Oscillation results for difference equations with several oscillating coefficients, Applied Mathematics and Computation, 251 (2015) , 81-91.  doi: 10.1016/j.amc.2014.11.045.
      G. E. Chatzarakis , Ch. G. Philos  and  I. P. Stavroulakis , On the oscillation of the solutions to linear difference equations with variable delay, Electron. J. Differ. Equ., 50 (2008) , 1-15. 
      G. E. Chatzarakis  and  Ö. Öcalan , Oscillation of difference equations with non-monotone retarded arguments, Applied Mathematics and Computation, 258 (2015) , 60-66.  doi: 10.1016/j.amc.2015.01.110.
      G. E. Chatzarakis, H. Péics, S. Pinelas and I. P. Stavroulakis, Oscillation results for difference equations with oscillating coefficients Advances in Difference Equations 2015 (2015), 17pp. doi: 10.1186/s13662-015-0391-0.
      L. H. Erbe  and  B. G. Zhang , Oscillation of discrete analogues of delay equations, Differential Integral Equations, 2 (1989) , 300-309. 
      G. Grzegorczyk  and  J. Werbowski , On oscillatory solutions of certain difference equations, Opuscula Mathematica, 26 (2006) , 317-326. 
      G. Grzegorczyk  and  J. Werbowski , Oscillation of higher-order linear difference equations, Comput. Math. Appl., 42 (2001) , 711-717.  doi: 10.1016/S0898-1221(01)00190-0.
      I. Györi and G. Ladas, Oscillation Theory of Delay Differential Equations with Applications Clarendon Press, Oxford, New York, 1991.
      W. G. Kelley and A. C. Peterson, Difference Equations. An Introduction with Applications Second edition, Harcourt/Academic Press, San Diego, CA, 2001.
      G. Ladas , Ch. G. Philos  and  Y. G. Sficas , Sharp conditions for the oscillation of delay difference equations, J. Appl. Math. Simulation, 2 (1989) , 101-111.  doi: 10.1155/S1048953389000080.
      J. Migda, Approximative solutions of difference equations, Electron. J. Qual. Theory Differ. Equ. 13 (2014), 26 pp.
      M. Migda , Existence of nonoscillatory solutions of some higher order difference equations, Appl. Math. E-Notes, 4 (2004) , 33-39. 
      M. Migda  and  J. Migda , On the asymptotic behavior of solutions of higher order nonlinear difference equations, Nonlinear Analysis, 47 (2001) , 4687-4695.  doi: 10.1016/S0362-546X(01)00581-8.
      M. Migda , Asymptotic properties of nonoscillatory solutions of higher order neutral difference equations, Opuscula Mathematica, 26 (2006) , 507-514. 
      W. Nowakowska  and  J. Werbowski , On connections between oscillatory solutions of functional, difference and differential equations, Fasc. Math., 44 (2010) , 95-106. 
      Ch. G. Philos , I. K. Purnaras  and  I. P. Stavroulakis , Sufficient conditions for the oscillation of delay difference equations, J. Difference Equ. Appl., 10 (2004) , 419-435.  doi: 10.1080/10236190410001648239.
      J. Werbowski , Bounded oscillations of differential equations generated by deviating arguments, Utilitas Math., 31 (1987) , 191-198. 
      A. Wyrwińska , Oscillation criteria of a higher order linear difference equation, Bull. Inst. Math. Acad. Sinica, 22 (1994) , 259-266. 
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