Nonlinear Singular First Order Partial Differential Equations Whose Characteristic Exponent Takes a Positive Integral Value

  • Hideshi Yamane

    University of Tokyo, Japan

Abstract

We consider nonlinear singular partial differential equations of the form .

It has been proved by Gérard and Tahara that there exists a unique holomorphic solution with if the characteristic exponent avoids positive integral values. In the present paper we consider what happens if takes a positive integral value at . Genetically, the solution is singular along the analytic set , , and we investigate how far it can be analytically continued.

Cite this article

Hideshi Yamane, Nonlinear Singular First Order Partial Differential Equations Whose Characteristic Exponent Takes a Positive Integral Value. Publ. Res. Inst. Math. Sci. 33 (1997), no. 5, pp. 801–811

DOI 10.2977/PRIMS/1195145018