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The differential counting polynomial. (English) Zbl 1386.12007

Summary: The aim of this paper is a quantitative analysis of the solution set of a system of polynomial nonlinear differential equations, both in the ordinary and partial case. Therefore, we introduce the differential counting polynomial, a common generalization of the dimension polynomial and the (algebraic) counting polynomial. Under mild additional assumptions, the differential counting polynomial decides whether a given set of solutions of a system of differential equations is the complete set of solutions.

MSC:

12H05 Differential algebra
34G20 Nonlinear differential equations in abstract spaces
35A01 Existence problems for PDEs: global existence, local existence, non-existence
35A10 Cauchy-Kovalevskaya theorems
35G20 Nonlinear higher-order PDEs
35Q30 Navier-Stokes equations
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References:

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