Gevrey Asymptotic Representation of the Solutions of Equations with One Turning Point

✍ Scribed by Karen Yagdjian

• Publisher: John Wiley and Sons
• Year: 1997
• Tongue: English
• Weight: 740 KB
• Volume: 183
• Category: Article
• ISSN: 0025-584X
• DOI: 10.1002/mana.19971830117

✦ Synopsis

Abstract

An ordinary differential equation of the type
magnified image
with parameterξ ϵ IR^n^ and smooth coefficients a__~j,a~__ ϵ C^∞^([‐T,T]) is studied. It is assumed that all the characteristic roots of the equation vanish at t = 0 while for t ≠ 0 they are real and distinct. The constructions of real‐valued phase functions ϕ__pH~kl~__ (k,l = 1., m) and of amplitude functions A~jkl~ such that for a given s ϵ [‐T, T] every solution u(t, ξ) of the equation can be represented as magnified image
where Ψ~j~(s, ξ)= D^j^~t~u(s,ξ), j = 0,m‐1 are given.