Convergence of formal solutions of first order singular partial differential equations of nilpotent type

Masatake Miyake; Akira Shirai

Banach Center Publications, Tome 97 (2012), p. 91-99 / Harvested from The Polish Digital Mathematics Library

Résumé

Let (x,y,z) ∈ ℂ³. In this paper we shall study the solvability of singular first order partial differential equations of nilpotent type by the following typical example: $P u (x, y, z) : = (y \partial_{x} - z \partial_{y}) u (x, y, z) = f (x, y, z) \in_{x, y, z}$ , where $P = y \partial_{x} - z \partial_{y} :_{x, y, z} \to_{x, y, z}$ . For this equation, our aim is to characterize the solvability on $_{x, y, z}$ by using the Im P, Coker P and Ker P, and we give the exact forms of these sets.

Publié le : 2012-01-01

Zbl 1262.35004

EUDML-ID : urn:eudml:doc:281602

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     author = {Masatake Miyake and Akira Shirai},
     title = {Convergence of formal solutions of first order singular partial differential equations of nilpotent type},
     journal = {Banach Center Publications},
     volume = {97},
     year = {2012},
     pages = {91-99},
     zbl = {1262.35004},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-bc97-0-6}
}

Masatake Miyake; Akira Shirai. Convergence of formal solutions of first order singular partial differential equations of nilpotent type. Banach Center Publications, Tome 97 (2012) pp. 91-99. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-bc97-0-6/