Structure of solutions of nonlinear partial differential equations of Gérard-Tahara type (Q2574360)

Summary: Let us consider the following nonlinear singular partial differential equation \[ (t,\partial/\partial t)^m u= F\biggl(t,x,\bigl\{(t\partial/\partial t)^j(\partial/\partial )^\alpha u\bigr\}_{j+|\alpha|\leq m,j< m}\biggr) \] in the complex domain. When the equation is of Fuchsian type with respect to \(t\), holormorphic and singular solutions were investigated quite well by Gérard-Tahara under some assumptions on characteristic exponents. In this paper, the same type of equations is solved in the general case without any assumption on characteristic exponents.