Solvability and semi-cycle analysis of a class of nonlinear systems of difference equations

Abstract

An analysis of semi-cycles of positive solutions to eight systems of difference equations of the following form. (Formula presented.) where a ∈ [0, + ∞), the sequences pn, qn, rn, sn are some of the sequences xn and yn, with positive initial values x−j,y−j, j = 1,2, is conducted in detail, and it is shown that these systems can be solved in closed-form, which is the main result here. Two methods for showing the solvability are described.