The Gevrey asymptotics in the case of singular perturbations

DOI10.1006/jdeq.2000.3787zbMath0968.34040OpenAlexW1987582641MaRDI QIDQ1584727

Yasutaka Sibuya

Publication date: 5 November 2000

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

Full work available at URL: https://doi.org/10.1006/jdeq.2000.3787

zbMATH Keywords

singular perturbationasymptotic solutionGevrey asymptotic

Mathematics Subject Classification ID

Asymptotic theory of functional-differential equations (34K25) Singular perturbations for ordinary differential equations (34E15) Asymptotic expansions of solutions to ordinary differential equations (34E05)

Related Items (11)

Deriving amplitude equations for weakly-nonlinear oscillators and their generalizations ⋮ Borel summability of divergent solutions for singularly perturbed first order ordinary differential equations ⋮ Gevrey normal forms for nilpotent contact points of order two ⋮ The Gevrey asymptotics in the initial value problem for singularly perturbed nonlinear differential equations ⋮ Entire extensions and exponential decay for semilinear elliptic equations ⋮ On singularly perturbed partial integro-differential equations with irregular singularity ⋮ Asymptotic existence theorems for formal power series whose coefficients satisfy certain partial differential recursions ⋮ Borel summability of divergent solutions for singular first-order partial differential equations with variable coefficients. I ⋮ Working with multiscale asymptotics ⋮ Formal power series solutions in a parameter ⋮ Multisummability of formal solutions of singular perturbation problems

Cites Work

• Basic theory of ordinary differential equations
• Asymptotic decomposition of systems of linear differential equations having poles with respect to a parameter
• On a conjecture of Wolfgang Wasow in linear turning point theory
• Gevrey solutions of singularly perturbed differential equations
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