On the Uniqueness Theorem for Nonlinear Singular Partial Differential Equations

The paper proves a uniqueness theorem of the solution of nonlinear singular partial differential equations % $$(t \partial / \partial t)^m u = F \left( t,x, \{(t \partial / \partial t)^j (\partial / \partial x)^{α} u \}_{j+|α| \leq m, j< 0$ for $i=1, \ldots, m$, a uniqueness theorem was proved in Tahara \cite{6}. The present paper discusses the case where $\text{Re}\, λ_i(x) \leq 0$ holds in a neighborhood of $x=0$ for $i=1, \ldots, m$. The result is applied to the problem of removable singularities of the solution