On a Functional-Differential Equation of A. F. Beardon and Functional-Differential Equations of Briot-Bouquet Type

摘要

We look for solutions of the functional-differential equation f(φ(z)) = a(z)f(z)f'(z) for given series φ and a. We show that all formal solutions / of this equation are local analytic. In order to do this we transform the equation to a special type of Briot-Bouquet differential equation.