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(∂u/∂t)=F(t,x,u,∂u/∂x) with (t,x)∈ℝ×ℂ under the assumption that F(t,x,z1,z2) 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.