Let us consider the following nonlinear singular partial differential equation in the complex domain with two independent variables . When the equation is of totally characteristic type, this equation was solved in  and  under certain Poincaré condition. In this paper, the author will prove the uniqueness of the solution under the assumption that is holomorphic in for some , , and that it satisfies (as ) uniformly in for some . The result is applied to the problem of removable singularities of the solution.
Hidetoshi TAHARA. "Uniqueness of the solution of nonlinear totally characteristic partial differential equations." J. Math. Soc. Japan 57 (4) 1045 - 1065, October, 2005. https://doi.org/10.2969/jmsj/1150287303