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Analytic continuation of solutions of some nonlinear convolution partial differential equations

Tahara H.

Opuscula Mathematica

2015

Vol. 35, no. 5

739--773

The paper considers a problem of analytic continuation of solutions of some nonlinear convolution partial differential equations which naturally appear in the summa-bility theory of formal solutions of nonlinear partial differential equations. Under a suitable assumption it is proved that any local holomorphic solution has an analytic extension to a certain sector and its extension has exponential growth when the variable goes to infinity in the sector.