Analytic Solutions of an Iterative Functional Differential Equation near Resonance

الملخص EN

We investigate the existence of analytic solutions of a class of second-order differential equations involving iterates of the unknown function x′′(z)+cx′(z)=x(az+bx(z)) in the complex field ℂ.

By reducing the equation with the Schröder transformation to the another functional differential equation without iteration of the unknown function λ2g′′(λz)g′(z)−λg′(λz)g′′(z) + c(g′(z))2(λg′(λz)−ag′(z)) = (g′(z))3(g(λ2z)−ag(λz)), we get its local invertible analytic solutions.