Mohammed Benalili

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.
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