Asymptotic existence theorems for formal power series whose coefficients satisfy certain partial differential recursions

DOI10.1016/j.jde.2004.10.007zbMath1144.34349OpenAlexW2040127864MaRDI QIDQ1763212

Werner Balser

Publication date: 22 February 2005

Published in: Journal of Differential Equations (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jde.2004.10.007

zbMATH Keywords

Partial differential equationsAsymptotic expansionsOrdinary differential equationsPower series solutionsMultisummability

Mathematics Subject Classification ID

Series solutions to PDEs (35C10) Perturbations, asymptotics of solutions to ordinary differential equations (34E10) Singular perturbations for ordinary differential equations (34E15) Stokes phenomena and connection problems (linear and nonlinear) for ordinary differential equations in the complex domain (34M40) Initial value problems for PDEs and systems of PDEs with constant coefficients (35E15)

Related Items (1)

Asymptotic existence theorem for formal solutions with singularities of nonlinear partial differential equations via multisummability

Cites Work

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• Summability of formal power-series solutions of partial differential equations with constant coefficients
• Newton polygons and formal Gevrey indices in the Cauchy-Goursat-Fuchs type equations
• Divergent solutions of the heat equation: On an article of Lutz, Miyake and Schäfke
• An operator \(L=aI-D_ t^ j D_ x^{-j-\alpha}-D_ t^{-j} D_ x^{j+\alpha}\) and its nature in Gevrey functions
• Gevrey asymptotic theory for singular first order linear partial differential equations of nilpotent type. I
• Divergence property of formal solutions for singular first order linear partial differential equations
• The Gevrey asymptotics in the case of singular perturbations
• Gevrey asymptotic theory for singular first order linear partial differential equations of nilpotent type. II
• Formal power series solutions in a parameter
• Multisummability of formal solutions of singular perturbation problems
• Singular perturbation of linear systems with a regular singularity
• Multisummability of formal solutions of some linear partial differential equations
• Multisummability of formal power series solutions of partial differential equations with constant coefficients
• Formal power series and linear systems of meromorphic ordinary differential equations
• Newton polygons and gevrey indices for linear partial differential operators
• On the Borel summability of divergent solutions of the heat equation
• Convergent Liouville–Green expansions for second-order linear differential equations, with an application to Bessel functions
• Wiener-Hopf equation and Fredholm property of the Goursat problem in Gevrey space
• Borel resummation of formal solutions to nonlinear Laplace equations in 2 variables
• Convergence of formal solutions of first order singular nonlinear partial differential equations in the complex domain
• Gevrey solutions of singularly perturbed differential equations
• The Borel sum of divergent Barnes hypergeometric series and its application to a partial differential equation

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