# On a class of non linear differential operators of first order with singular point

## (*Lobachevskii Journal of Mathematics, Volume XVII*)

We consider the problem of the existence and uniqueness of solutions for partial differential operator of the form *Lu=D *_{X} u - B(x,u) where *X* is a vector field. The solvability of *L* may be of some interest since by the Nash-Moser inverse function theorem the equivalence problem in differential geometry can be solved via Lie derivative operator and the later is locally a particular case of *L*. An application to the equivalence of dynamic systems is given.