二阶线性差分方程非线性扰动解的渐近性质

Asymptotic behavior of solutions for nonlinear perturbations of linear second order difference equation

给出线性差分方程Δ2xn-1=anf(xn)的解渐近于其对应齐次方程主解的充分条件,并用方程的系数给出其渐近的精确表示.

This paper is concerned with the asymptotic behavior of solutions to the nonlinear perturbations of a nonoscillatory second order difference equation -Δ~2x_(n-1)=a_nf(x_n)-Under the assumption that the corresponding homogeneous equation is nonoscillatory,sufficient conditions established and the difference equation has solution that behave asymptotically like principal solutions of the homogeneous equation,then give its accurate expression with coefficients of the equation.