Borel summability of divergent solutions for singularly perturbed first order ordinary differential equations

DOI10.2748/tmj/1156256403zbMath1118.34083OpenAlexW1978611487MaRDI QIDQ854474

Masaki Hibino

Publication date: 4 December 2006

Published in: Tôhoku Mathematical Journal. Second Series (Search for Journal in Brave)

Full work available at URL: http://www.math.tohoku.ac.jp/tmj/tohokumathjen.html

zbMATH Keywords

singular perturbationanalytic continuationBorel summability

Mathematics Subject Classification ID

Asymptotics and summation methods for ordinary differential equations in the complex domain (34M30) Singular perturbation problems for ordinary differential equations in the complex domain (complex WKB, turning points, steepest descent) (34M60)

Related Items (4)

Gevrey normal forms for nilpotent contact points of order two ⋮ Singular perturbation of nonlinear systems with regular singularity ⋮ Borel summability of divergent solutions for singular first-order partial differential equations with variable coefficients. I ⋮ Borel summability of divergent solutions for singular first-order partial differential equations with variable coefficients. II

Cites Work

• Unnamed Item
• Unnamed Item
• From divergent power series to analytic functions. Theory and application of multisummable power series
• 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
• Multisummability of formal solutions of singular perturbation problems
• Singular perturbation of linear systems with a regular singularity
• Summability of divergent series
• Formal power series and linear systems of meromorphic ordinary differential equations
• On the Borel summability of divergent solutions of the heat equation
• Gevrey solutions of singularly perturbed differential equations

This page was built for publication: Borel summability of divergent solutions for singularly perturbed first order ordinary differential equations