The authors are concerned with the difference equation where for k a positive integer. A sufficient condition for the oscillation of all solutions of (*) is presented in the form
In the third part of the paper a sufficient condition for the existence of a positive solution y of (*) such that is given. For a similar problem see e.g. the reviewer and B. Szmanda [Demonstr. Math. 17, 153-164 (1984; Zbl 0557.39004)].