Existence of positive solutions of systems of Volterra nonlinear difference equations

In this paper, a classification scheme for eventually positive solutions of a class of two-dimensional Volterra nonlinear difference equations is given in terms of asymptotic magnitudes. Some necessary as well as sufficient conditions for the existence of such solutions are provided without any monotonicity conditions on the nonlinear term. Published in Neliniini Kolyvannya, Vol. 9, No. 1, pp. 37–47, January–March, 2006.