A critical case of stability of one quasilinear difference equation of the second order期刊界 All Journals 搜尽天下杂志传播学术成果专业期刊搜索期刊信息化学术搜索

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A critical case of stability of one quasilinear difference equation of the second order

Authors:

I E Vitrichenko

Institution:

(1) Odessa University, Odessa

Abstract:

We obtain sufficient conditions for the Perron stability of the trivial solution of a real difference equation of the form

$y_{n + 1} - 2\lambda _n y_n + y_{n - 1} = F(n,y_n ,\Delta y_{n - 1} ), n \in N$

where $y_n \in \left] { - 1,1} \right,\left| {F(n,y_n ,\Delta y_{n - 1} )} \right| \le L_n \left( {\left| {y_n \left| + \right|\Delta y_{n - 1} } \right|} \right)^{1 + \alpha } ,L_n \ge 0$ and $\alpha \in \left] {0, + \infty } \right$ . The resuits obtained are valid for the case where $\left| {\lambda _n } \right| = 1 + o(1), n \to + \infty$ . Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 51, No. 12, pp. 1593–1603, December, 1999.

Keywords:

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