Solvability of partial differential equations of nonlinear totally characteristic type with resonances (Q1425468)

The author considers the following nonlinear singular partial differential equation \[ (t\partial/ \partial t)^mu=F(t,x, \{(t \partial/ \partial t)^j(\partial/ \partial x)^\alpha u)_{j+|\alpha |\leq m,j<m} \}) \] in the complex domain. When the equation is of totally characteristic type, he proved already with H. Chen the existence of the unique holomorphic solution provided that the equation satisfies the Poincaré condition and that no resonances occur. In this paper he solves the same equation in the case where some resonances occur.