Publications of the Research Institute for Mathematical Sciences
Online ISSN : 1663-4926
Print ISSN : 0034-5318
Nonlinear Singular First Order Partial Differential Equations Whose Characteristic Exponent Takes a Positive Integral Value
Hideshi Yamane
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1997 年 33 巻 5 号 p. 801-811

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We consider nonlinear singular partial differential equations of the form (tDt−ρ(x))u=ta(x)+G2(x) (t, tDtu, u, D1u, .., Dnu).
It has been proved by Gérard and Tahara that there exists a unique holomorphic solution with u(0, x)≡0 if the characteristic exponent ρ(x) avoids positive integral values. In the present paper we consider what happens if ρ(x) takes a positive integral value at x=0. Genetically, the solution u(t, x) is singular along the analytic set {t=0, ρ(x)∈N*}, N*={1, 2, ..}, and we investigate how far it can be analytically continued.

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