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Original Articles

Results and problems about solutions of perturbed Lyness' type order k difference equations in , with examples, and test of the efficiency of a quasi-Lyapunov function method

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Pages 1331-1352 | Received 06 Jan 2012, Accepted 04 Oct 2012, Published online: 08 Jan 2013

References

  • Bastien , G. and Rogalski , M. 2004 . New method for the study of solutions of the difference equation . Radovi Matematički , 12 : 135 – 152 .
  • Bastien , G. and Rogalski , M. 2004 . Global behaviour of the solutions of Lyness' difference equations . J. Difference Equ. Appl. , 10 : 977 – 1003 .
  • Bastien , G. and Rogalski , M. 2004 . On some algebraic difference equations in , related to families of conics or cubics: Generalization of the Lyness' sequences . J. Math. Anal. Appl. , 300 : 303 – 333 .
  • Bastien , G. and Rogalski , M. 2005 . On the algebraic difference equation in related to a family of elliptic quartics in the plane . Adv. Difference Equ. , 3 : 227 – 261 .
  • Bastien , G. and Rogalski , M. Results and conjectures about order q Lyness' difference equation in , with a particular study of the case q = 3 . Adv. Difference Equ. , 2009 (2009), 36 pp., article no. 134749
  • Basu , S. and Merino , O. Global behavior of solutions to two classes of second-order rational difference equations . Adv. Difference Equ. , 2009 (2009), article no. 128602
  • Beukers , F. and Cushman , R. 1998 . Zeeman's monotonicity conjecture . J. Differ. Equ. , 143 : 191 – 200 .
  • Camouzis , E. and Ladas , G. 2007 . Dynamics of Third-Order Rational Difference Equations with Open Problems and Conjectures , Boca Raton, FL : Chapman & Hall/CRC Press .
  • Cima , A. , Gasull , A. and Maosa , V. 2007 . Dynamics of the third order Lyness' difference equation . J. Difference Equ. Appl. , 13 ( 10 ) : 855 – 884 .
  • Cima , A. , Gasull , A. and Maosa , V. 2008 . Some properties of the k-dimensional Lyness' map . J. Phys. A Math. Theor. , 41 : 285205
  • El-Morshedy , H.-A. 2004 . The global attractivity of difference equations of nonincreasing nonlinearities with applications . Comput. Math. Appl. , 45 : 749 – 758 .
  • Grove , E.A. , Jarrowski , E.J. , Kent , C.M. and Ladas , G. 1994 . On the rational recursive sequence . Commun. Appl. Nonlinear Anal. , 1 ( 3 ) : 61 – 72 .
  • Kočic , V.L. and Ladas , G. 1993 . Global Behavior of Nonlinear Difference Equations of Higher Order with Applications , Dordrecht : Kluwer Academic Publishers .
  • Lyness , R.C. 1942 . Notes 1581, 1847 and 2952 . Math. Gaz. , 26 : 62 29 (1945), p. 231; and 45 (1961), p. 201
  • Merino , O. 2011 . Global attractivity of the equilibrium of a difference equation: An elementary proof assisted by computer algebra system . J. Difference Equ. Appl. , 17 ( 1 ) : 34 – 41 .
  • Palladino , F. 2009 . On the characterization of rational difference equations . J. Difference Equ. Appl. , 15 ( 3 ) : 253 – 260 .
  • Zeeman , E.C. 1996 . Geometric Unfolding of a Difference Equation , Oxford : Hertford College . Unpublished paper

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