Uniqueness of the solution of some nonlinear singular partial differential equations of the second order

TL;DR

This paper proves the uniqueness of solutions for certain nonlinear second-order Fuchsian PDEs in the complex domain and applies this to the analytic continuation of local holomorphic solutions.

Contribution

It establishes a weak-assumption-based uniqueness result for nonlinear Fuchsian PDEs and demonstrates its application to analytic continuation problems.

Findings

Uniqueness of solutions under weak assumptions

Application to analytic continuation of holomorphic solutions

Advancement in understanding nonlinear Fuchsian PDEs

Abstract

In this paper, we consider a nonlinear Fuchsian type partial differential equation of the second order in the complex domain. Under a very weak assumption, we show the uniqueness of the solution. The result is applied to the problem of analytic continuation of local holomorphic solutions of this equation.