2019/12/23 by Matthias Stiefenhofer, Stiefenhofer, Matthias
Mathematics · Physics and Astronomy · #Algebraic Geometry (math.AG) #FOS: Mathematics #Fractional Differential Equations Solutions #Nonlinear Waves and Solitons #Numerical methods for differential equations #math.AG
paper · pdf · doi:10.48550/arxiv.1912.10735
15 pages
arxiv created 2019/12/23 · openalex publication_date 2019/12/23 · arxiv updated 2019/12/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In [DL] systems of differential polynomials are investigated with respect to properties of Artin approximation type. The key tool in [DL] is an extended version of a formula by Hurwitz [Hu] expressing high order derivatives of an expansion by lower ones. The formula is further refined in [VFZ] to deliver sufficient conditions concerning the existence of power series solutions of scalar algebraic differential equations of order n. In the paper at hand, the main results from [VFZ] are first reproduced and further extended to systems of nonlinear differential algebraic equations. In addition, a simple extension of Tougeron's implicit function theorem is given in a specific constellation. The results follow from [S1], [S2] where Artin approximation is treated within a Banach space setting, thereby constructing an expansion formula that expresses accurately the required dependency of low and high order derivatives within the system of undetermined coefficients.