Authors: | Stević, Stevo Diblík, Josef Iričanin, Bratislav Šmarda, Zdenk |

Affiliations: | Mathematical Institute of the Serbian Academy of Sciences and Arts |

Title: | On a third-order system of difference equations with variable coefficients |

Journal: | Abstract and Applied Analysis |

Volume: | 2012 |

Issue Date: | 20-Jun-2012 |

Rank: | M21a |

ISSN: | 1085-3375 |

DOI: | 10.1155/2012/508523 |

Abstract: | We show that the system of three difference equations x n+1 = a n(1) x n-2/(b n(1) y n z n-1 x n-2 + c n(1)), y n+1 = a n(2) y n-2/(b n(2) z n x n-1 y n-2 + c n(2)), and z n+1 = a n(3) z n-2 /(b n(3) x n y n-1 z n-2 + c n(3)), n N 0, where all elements of the sequences a n(i), b n(i), c n(i), n N 0, i { 1,2, 3 }, and initial values x -j, y -j, z -j, j { 0,1, 2 }, are real numbers, can be solved. Explicit formulae for solutions of the system are derived, and some consequences on asymptotic behavior of solutions for the case when coefficients are periodic with period three are deduced. |

Publisher: | Hindawi |

Project: | Development Programme of The Ministry of Education,Youth and Sports of Czech Republic no. 25/16—PoZaP—Support for Foreign Teachers Council of Czech Government, Grant MSM 00216 30519 Brno University of Technology, Grant FEKT-S-11-2-921 Modulation of intracellular energy balance-controlling signalling pathways in therapy of cancer and neuro-immuno-endocrine disorders Development of new information and communication technologies, based on advanced mathematical methods, with applications in medicine, telecommunications, power systems, protection of national heritage and education Physical and functional effects of radiation interaction with electrotechnical and biological systems |

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