Multisummability of formal power series solutions of nonlinear partial differential equations in complex domains

Let $\hat{u}(t,x)=\sum_{n=1}^{\infty}u_{n}(x)t^{n},\ (t,x)\in \mathbb{C}\times \mathbb{C}^{d}$ , be a formal power series solution of a nonlinear partial differential equation. We study multisummability of $\hat{u}(t,x)$ . This paper is a continuation of [S. Ōuchi, Multisummability of formal solutions of some linear partial differential equations, J. Differential Equations 185 (2002), 513–549], where linear partial differential equations were treated.