A note on positive non - oscillatory solutions of the difference equation xn 1 1 5 a 1 xp n 2 k x
نویسنده
چکیده
where a . 21, p . 0 and k [ N is fixed, has positive non-oscillatory solutions which converge to the positive equilibrium x 1⁄4 aþ 1: This result solves Open Problem 1 in Stević, 2005, On the recursive sequence xnþ1 1⁄4 aþ ðxpn21=xnÞ; Journal of Applied Mathematics and Computing 18(1–2), 229–234, as well as, Open Problem 1 in DeVault, Kent and Kosmala, 2003, On the recursive sequence xnþ1 1⁄4 pþ ðxn2k=xnÞ; Journal of Difference Equations and Application, 9(8), 721–730. It is interesting that the method described here can, in some cases, be applied also when the parameter a is variable.
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