Formal and convergent solutions of singular partial differential equations

DOI10.1007/BF01170931zbMath0502.35006OpenAlexW4253721471MaRDI QIDQ1172742

Raymond Gerard, Gunter Bengel

Publication date: 1982

Published in: Manuscripta Mathematica (Search for Journal in Brave)

Full work available at URL: https://eudml.org/doc/154864

zbMATH Keywords

existenceformal power seriesNewton iteration processconvergent series solutionsconvergent transformations of singular vector fieldssingular partial differential equations

Mathematics Subject Classification ID

Analyticity in context of PDEs (35A20) Series solutions to PDEs (35C10) Nonlinear higher-order PDEs (35G20) Theoretical approximation in context of PDEs (35A35) Linear higher-order PDEs (35G05) Implicit function theorems; global Newton methods on manifolds (58C15)

Related Items

Blow-up surfaces for nonlinear wave equations, II ⋮ Necessary and sufficient condition for the convergence of formal solutions ⋮ Convergence of formal solutions for Fuchs-Goursat equations ⋮ Unnamed Item ⋮ Polygône de Newton et $b$-fonctions pour les modules microdifférentiels ⋮ Holomorphic and singular solutions of nonlinear singular first order partial differential equations

Cites Work

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• On a class of linear partial differential equations whose formal solutions always converge
• On the solutions of analytic equations
• Stable and Random Motions in Dynamical Systems
• Formal and Convergent Power Series Solutions of Singular Partial Differential Equations
• Generalized implicit function theorems with applications to some small divisor problems, I
• On the theorem of Cauchy-Kowalevsky for first order linear differential equations with degenerate principal symbols

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