## Mohammed Benalili

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

## (Lobachevskii Journal of Mathematics, Vol.17, pp.25 - 41)

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.

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