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=DXu-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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