## Solutions of the equation $$f_y u_x-f_xu_y=g$$.(English)Zbl 0919.35031

Summary: We study locally, on a neighborhood of an isolated singular point, the existence of solutions of the partial differential equation $$f_y u_x-f_x u_y= g$$, in the real analytic case. We suppose that the function $$f$$ has a minimum at the origin.

### MSC:

 35F05 Linear first-order PDEs 35A20 Analyticity in context of PDEs

### Keywords:

isolated singular point
Full Text:

### References:

 [1] Arnold, V.), Varchenko, A.) and Goussein-Zade, S.) .- Singularités des applications différentiables, 2e partie, Monodromie et comportement asymptotiques des intégrales, Éditions Mir - Moscou, 1986. [2] Brieskorn, E.) . - Die Monodromie der isolierten Singularitäten von Hyperflächen, Manuscripta Math.2 (1970), pp. 103-161. · Zbl 0186.26101 [3] Malgrange, B.) . - Intégrales asymptotiques et monodromie, Ann. Scient. Éc. Sup., série 4, 7 (1974), pp. 405-430. · Zbl 0305.32008 [4] Malgrange, B.) . - Sur les points singuliers des équations différentielles, L’Enseignement Math.20 (1974), pp. 147-176. · Zbl 0299.34011 [5] Milnor, J.) . - Singular points of Complex Hypersurfaces, Annals of Mathematics Studies, Princeton University Press, Princeton, New Jersey, 61 (1968). · Zbl 0184.48405
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.