On Global Attractivity of a Class of Nonautonomous Difference Equations

We mainly investigate the global behavior to the family of higher-order nonautonomous recursive equations given by yn p ryn−s / q φn yn−1, yn−2, . . . , yn−m yn−s , n ∈ N0, with p ≥ 0, r, q > 0, s,m ∈ N and positive initial values, and present some sufficient conditions for the parameters andmaps φn : R m → R , n ∈ N0, under which every positive solution to the equation converges to zero or a unique positive equilibrium. Our main result in the paper extends some related results from the work of Gibbons et al. 2000 , Iričanin 2007 , and Stević vol. 33, no. 12, pages 1767–1774, 2002; vol. 6, no. 3, pages 405–414, 2002; vol. 9, no. 4, pages 583–593, 2005 . Besides, several examples and open problems are presented in the end.