On the Existence and the Asymptotic Behavior of Nonoscillatory Solutions of Second Order Quasilinear Difference Equations

抄録

For the second-order quasilinear difference equation Δ (p_n|Δx_n|^α–1Δx_n) + q_n|x_{n + 1}|^β–1x_{n + 1} = 0, α > β, we establish a necessary and sufficient condition for the existence of slowly growing and slowly decaying positive solution. In particular, when p_n = 1, the precise asymptotic forms of its slowly growing positive solutions are obtained.