On a class of singular nonlinear first order partial differential equations

Abstract

In this paper, we consider a class of singular nonlinear first order partial differential equations $t(\partial u/\partial t)=F(t,x,u,\partial u/\partial x)$ with $(t,x)\in \mathbb{R}\times \mathbb{C}$ under the assumption that $F(t,x,z_1,z_2)$ is a function which is continuous in $t$ and holomorphic in the other variables. Under suitable conditions, we determine all the solutions of this equation in a neighborhood of the origin.