A critical case of stability of one quasilinear difference equation of the second order - Vitrychenko, I. E. (Ukrains’kyi Matematychnyi Zhurnal, 1999)
We obtain sufficient conditions for the Perron stability of the trivial solution of a real difference equation of the form y_n + 1 - 2λ _n y_n + y_n - 1 = F(n,y_n ,Δ y_n - 1 ), n N where \(y_n ] - 1,1 [,| F(n,y_n ,Δ y_n - 1 ) | L_n ( | y_n | + |Δ y_n - 1 | )^1 + α ,L_n 0\) and \(α ] 0, + ∞ [\) . The resuits obtained are valid for the case where \(| λ _n | = 1 + o(1), n → + ∞ \) .