Open AccessOn a solvable class of product-type systems of difference equations
Author(s) -
Stevo Stević,
Bratislav Iričanin,
Zdeněk Šmarda
Publication year - 2017
Publication title -
filomat
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.449
H-Index - 34
eISSN - 2406-0933
pISSN - 0354-5180
DOI - 10.2298/fil1719113s
Subject(s) - mathematics , product (mathematics) , type (biology) , class (philosophy) , polynomial , product type , pure mathematics , combinatorics , mathematical analysis , geometry , ecology , artificial intelligence , computer science , biology , programming language
It is shown that the following class of systems of difference equations zn+1 = ?zanwbn, wn+1 = ?wcnzdn-2, n ? N0, where a,b,c,d ? Z, ?, ?, z-2, z-1, z0,w0 ? C \ {0}, is solvable, continuing our investigation of classification of solvable product-type systems with two dependent variables. We present closed form formulas for solutions to the systems in all the cases. In the main case, when bd ? 0, a detailed investigation of the form of the solutions is presented in terms of the zeros of an associated polynomial whose coefficients depend on some of the parameters of the system.