Unbounded Solutions of the Difference Equation xn=xn−lxn−k−1 - Stevo Stević; Bratislav Iričanin (Abstract and Applied Analysis)
The following difference equation xn=xn−lxn−k−1, n∈ℕ0, where k,l∈ℕ, k<l, gcd(k,l)=1, and the initial values x-l,…,x-2,x-1 are real numbers, has been investigated so far only for some particular values of k and l. To get any general result on the equation is turned out as a not so easy problem. In this paper, we give the first result on the behaviour of solutions of the difference equation of general character, by describing the long-term behavior of the solutions of the equation for all values of parameters k and l, where the initial values satisfy the following condition min{x-l,…,x-2,x-1}.