Geodesic
On a class of non linear differential operators of first order with singular point
Lobachevskii journal of mathematics, Tome 17 (2005), pp. 25-41 Cet article a éte moissonné depuis la source Math-Net.Ru

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We consider the problem of the existence and uniqueness of solutions for partial differential operator of the form $Lu=D_Xu-B(x,u)$ 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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     title = {On a class of non linear differential operators of first order with singular point},
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M. Benalili. On a class of non linear differential operators of first order with singular point. Lobachevskii journal of mathematics, Tome 17 (2005), pp. 25-41. http://geodesic.mathdoc.fr/item/LJM_2005_17_a2/

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