Movable singular points of ordinary differential equations with algebraic singularities of the right-hand side

Abstract

Consider the differential equation w(n) = F (w(n−1), w(n−2), . . . , w, z) , (1) where n ∈ N and F is an analytic function. In the present paper, we obtain conditions that must necessarily be satisfied by the algebraic singularities of F if Eq. (1) has no movable critical singular points.