Global Behavior of Rational Sequences Involving Piecewise Power Function
Tóm tắt
In this paper, we are concerned with the global behavior ofthe solutions of the difference equation
$$x_{n + 1} = \frac{{f\left( {x_n } \right)}}{{x_{n - 1} }},n \geqslant 1,\quad x_0 ,x_1 > 0$$
where
$$f\left( x \right) = \left\{ \begin{gathered} x^a ,\quad 0 < x < 1 \hfill \\ x^b ,\quad 0 \leqslant x < \infty , \hfill \\ \end{gathered} \right.$$
and
$$a,b \geqslant 0$$
. Necessary and sufficient conditions for boundedness, persistence,and periodicity of all solutions will be established. The oscillatorybehavior will be investigated.
Tài liệu tham khảo
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