On one method for the analysis of the Cauchy problem for a singularly perturbed inhomogeneous second-order linear differential equation

2017 ◽  
Vol 57 (10) ◽  
pp. 1635-1649
Author(s):  
E. E. Bukzhalev
Keyword(s):  
Differential Equation ◽  
Cauchy Problem ◽  
Linear Differential Equation ◽  
Second Order ◽  
Singularly Perturbed ◽  
Order Linear Differential Equation ◽  
Order Linear ◽  
The Cauchy Problem ◽  
Linear Differential

A property of the asymptotic series for a class of Titchmarsh–Weyl m-functions

1986 ◽  
Vol 102 (3-4) ◽  
pp. 253-257 ◽  
Author(s):  
B. J. Harris
Keyword(s):  
Differential Equation ◽  
Asymptotic Expansion ◽  
Linear Differential Equation ◽  
Asymptotic Series ◽  
Second Order ◽  
Order Linear Differential Equation ◽  
Order Linear ◽  
The Real ◽  
Linear Differential ◽  
Image Position

SynopsisIn an earlier paper [6] we showed that if q ϵ CN[0, ε) for some ε > 0, then the Titchmarsh–Weyl m(λ) function associated with the second order linear differential equationhas the asymptotic expansionas |A| →∞ in a sector of the form 0 < δ < arg λ < π – δ.We show that if the real valued function q admits the expansionin a neighbourhood of 0, then

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