Abstract
Solvable product-type system of difference equations whose associated polynomial is of the fourth order
Highlights
Concrete nonlinear difference equations and systems is a research field of some recent interest
Some of them are solved by the method of transformation
An interesting related method has been recently applied to partial difference equations in [29] and [32]
Summary
Concrete nonlinear difference equations and systems is a research field of some recent interest (see, e.g., [2,4,9,10,11,12,13,14,15,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45]). The solvability of product-type systems with non-positive initial values and coefficients is a problem of interest. The max-type system in [23] is solved by reducing it to a product-type one They appeared indirectly in the study of some max-type and related difference equations and systems, as their boundary cases (see, e.g., [19, 20, 37]). In the main case when bd = 0, a polynomial of the fourth order is associated to the system, and its solutions are represented in terms of the parameters, through the roots of the polynomial in all the cases (the roots are given in terms of parameters a, b, c, d), which is the main achievement of the paper.
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