On a Class of Nonautonomous Max-Type Difference Equations

On a Class of Nonautonomous Max-Type Difference Equations

and Applied Analysis 3 This paper is devoted to the study of the following nonautonomous max-type difference equation with two delays: xn max { fn x n−k , B x β n−m } , n ∈ N0, 1.7 where k,m ∈ N, α, β ∈ R are fixed and fn n∈N0 is a positive sequence with a finite limit. Inspired by the methods and proofs of the above-mentioned papers, here we try to find some sufficient conditions such that eve...

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 u...

On the periodic nature of some max-type difference equations

Recently there has been a lot of interest in studying the global attractivity, the boundedness character, and the periodicity nature of nonlinear difference equations. In [5, 6, 8] some global convergence results were established which can be applied to nonlinear difference equations in proving that every solution of these equations converges to a periodic solution (which need not necessarily b...

Global Attractivity of a Family of Max-Type Difference Equations

On meromorphic solutions of certain type of difference equations

‎We mainly discuss the existence of meromorphic (entire) solutions of‎ ‎certain type of non-linear difference equation of the form‎: ‎$f(z)^m+P(z)f(z+c)^n=Q(z)$‎, ‎which is a supplement of previous‎ ‎results in [K‎. ‎Liu‎, ‎L. Z‎. ‎Yang and X‎. ‎L‎. ‎Liu‎, ‎Existence of entire solutions of nonlinear difference‎ ‎equations‎, ‎Czechoslovak Math. J. 61 (2011)‎, no. 2, ‎565--576‎, and X‎. ‎G‎. ‎Qi‎...