Opuscula Math. 35, no. 5 (2015), 739-773
Analytic continuation of solutions of some nonlinear convolution partial differential equations
Abstract. The paper considers a problem of analytic continuation of solutions of some nonlinear convolution partial differential equations which naturally appear in the summability 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.
Keywords: convolution equations, partial differential equations, analytic continuation, summability, sector.
Mathematics Subject Classification: 45K05, 45G10, 35A20.
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- Communicated by P.A. Cojuhari.
- Received: 2013-12-01.
- Revised: 2014-12-12.
- Accepted: 2015-01-23.
- Published online: 2015-04-27.