On compatibility conditions and manilolds of solutions to one class of overdetermined systems of second order partial differential equations

R. Pirov

S. Aini Tajik State Pedagogical University

Abstract: In the work we consider a class of overdetermined system of second order partial differential equations with one unknown function involving one or two second order derivatives in the right hand side. We find the compatibility conditions and prove theorems on existence and uniqueness of solutions involving at most six arbitrary constants.

Keywords: overdetermined systems, compatbility conditions, manifolds of solutions, cross differentiation.

UDC: 517.9

MSC: 35N10

Received: 03.12.2015

 English version: Ufa Mathematical Journal, 2016, 8:2, 58–64

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