Checking existence of solutions of partial differential equations in the fields of Laurent series

Authors:
S. V. Paramonov
Affiliations:
Department of Computational Mathematics and Cybernetics, Moscow State University, Moscow, Russia 119991
Venue:
Programming and Computing Software
Year:
2014

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Abstract

It is proved that the problem of checking the existence of solutions of linear partial differential equations with polynomial coefficients is algorithmically undecidable. Decidability of the problem of checking the existence of monomial solutions with real and complex exponents is established.