A Sharp Form of the Uniqueness of the Solution to Nonlinear Totally Characteristic Partial Differential Equations

Abstract

The paper deals with the following nonlinear partial differential equation $(t \partial/\partial t)^m u = F (t,x, \{(t \partial/\partial t)^j (\partial/\partial x)^{\alpha} u\}_{j+\alpha \leq m, j<m} )$ with $(t,x) \in \mathbb{C}^2$ in the complex domain. Under the assumption that the equation is of totally characteristic type, the uniqueness of the solution was first proved in [4]. The present paper gives a sharp form of this uniqueness theorem.