Periodic solutions of second-order nonlinear difference equations containing a small parameter. II: Equivalent linearization
[For part I see ibid. 316, 273-277 (1983; Zbl 0529.39002).] The classical method of equivalent linearization is applied to obtain approximations to the periodic solutions of the following class of nonlinear difference equations \[ x_{k+1}-(2 \cos \phi)x_ k+x_{k- 1}=\epsilon f(x_ k,x_{k-1}) \] where \(k=0,1,2,...\); \(\phi\) is a given constant; f is a polynomial function of its arguments and \(0<\epsilon \ll 1\) is a small positive parameter.
scientific article; zbMATH DE number 3946794