On the summability of formal solutions for doubly singular nonlinear partial differential equations

Abstract

We study Gevrey asymptotic properties of solutions of singularly perturbed singular nonlinear partial differential equations of irregular type in the complex domain. We construct actual holomorphic solutions of these problems with the help of the Borel---Laplace transforms. Using the Malgrange---Sibuya theorem, we show that these holomorphic solutions have a common formal power series asymptotic expansion of Gevrey order 1 in the perturbation parameter.