In this paper we consider positive solutions of the following difference equation $$x_{n+l}\;=\;min[{\frac{A}{x_{n}},{\frac{B}{x_{n-2}}}],\;A,B\;>\;0$$. We prove that every positive solution is eventually periodic. Also, we present here some result...
In this paper we consider positive solutions of the following difference equation $$x_{n+l}\;=\;min[{\frac{A}{x_{n}},{\frac{B}{x_{n-2}}}],\;A,B\;>\;0$$. We prove that every positive solution is eventually periodic. Also, we present here some results concerning positive solutions of the difference equation $$x_{n+l}\;=\;min[{\frac{A}{x_{n}x_{n-1}{\cdots}x_{n-k}},{\frac{B}{x_{n-(k+2)}{\cdots}x_{n-(2k+2)}}],\;A,B\;>\;0$$.