Solving Ordinary Differential Equations in Terms of Series with Real Exponents

DOI10.2307/2001845zbMath0758.12004OpenAlexW2005941291MaRDI QIDQ3977244

Michael F. Singer, Dima Yu. Grigoriev

Publication date: 25 June 1992

Published in: Transactions of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.2307/2001845

zbMATH Keywords

undecidabilitydifferential polynomialgeneralized power series solutionsNewton polygon proceduresolutions of polynomial differential equations

Mathematics Subject Classification ID

Differential algebra (12H05) Ordinary differential equations in the complex domain (34M99) Formal power series rings (13F25)

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The branching problem in generalized power solutions to differential equations ⋮ On the convergence of generalized power series solutions of \(q\)-difference equations ⋮ Tropical differential equations ⋮ Multiplicity of the solutions of a differential polynomial ⋮ Unnamed Item ⋮ Power series solutions of non-linear \(q\)-difference equations and the Newton-Puiseux polygon ⋮ Finiteness property for generalized abelian integrals. ⋮ Rational solutions of high-order algebraic ordinary differential equations ⋮ Polygons of Petrović and Fine, algebraic ODEs, and contemporary mathematics ⋮ Ritt-Wu characteristic set method for Laurent partial differential polynomial systems ⋮ A polynomial time algorithm for finding rational general solutions of first order autonomous ODEs ⋮ Non-oscillating solutions of a differential equation and Hardy fields ⋮ The Maillet-Malgrange type theorem for generalized power series ⋮ A differential Puiseux theorem in generalized series fields of finite rank ⋮ Liouville closed \(H\)-fields ⋮ Tropical differential Gröbner bases ⋮ Existence and convergence of Puiseux series solutions for autonomous first order differential equations ⋮ Solving first order autonomous algebraic ordinary differential equations by places ⋮ Generalised power series solutions of sub-analytic differential equations ⋮ Formal solutions of differential equations ⋮ On existence and uniqueness of formal power series solutions of algebraic ordinary differential equations ⋮ Linked integral pencils

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