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.

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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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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/

[1] J. Gorowski, A. Zajtz, “On a class of linear differential operators of first order with singularity point”, Prace Matematyczne, 1997, no. 14, 129–140 | MR | Zbl

[2] Nelson, E., Topics in dynamics, I: Flows, Princeton, 1970 | MR

[3] Smale, S., “Differentiable dynamic systems”, Bulletin of the Amer. Math. Soc., 73 (1967), 747–817 | DOI | MR

[4] Wintner, A., “Bounded matrices and linear differential equations”, Amer. J. Math., 79 (1957), 139–151 | DOI | MR | Zbl

[5] Zajtz, A., “Some division theorems for vector fields”, Ann. Pol. Math., 1993, 19–28 | MR | Zbl