On boundedness of the solutions of the difference equation \(x_{n+1}=x_{n-1}/(p+x_{n})\)
Summary: We study the difference equation \(x_{n+1}=x_{n-1}/(p+x_n)\), \(n=0,1,\dots\), where initial values \(x_{-1},x_0\in(0,+\infty)\) and \(0<p<1\), and obtain the set of all initial values \((x_{-1},X_0)\in (0,+\infty)\times (0,+\infty)\) such that the positive solution \(\{x_n\}_{n=-1}^\infty\) is bounded. This answers the open problem 2 proposed by \textit{M. R. S. Kulenović} and \textit{G. Ladas} [Dynamics of second order rational difference equations. With open problems and conjectures. Boca Raton, FL: Chapman \& Hall/CRC (2002; Zbl 0981.39011)].
scientific article; zbMATH DE number 5304368