Analytic Solutions for a Class of Nonlinear Ordinary Differential Equations

In this article, existence and uniqueness of analytic solutions to a class of problems of the form $ zG^{\prime \prime }(z)+J(z)G^{\prime }(z)+F(G(z))=0, G(0)=G_0 $ are considered, where J is analytic in some neighborhood about 0 and F is analytic in some neighborhood of G 0 . This is a generalization of a class of problems considered by Rothe (F. Rothe (1997). A variant of Frobenius' method for the Emden-Fowler equation. Applicable Analysis , 66 , 227-245).