Asymptotics of solutions of a second-order linear differential system with a special right-hand side

1990 ◽  
Vol 31 (2) ◽  
pp. 260-263
Author(s):  
G. V. Kopylova ◽  
G. E. Samkova
Keyword(s):  
Differential System ◽  
Second Order ◽  
Linear Differential System ◽  
Asymptotics Of Solutions ◽  
Order Linear ◽  
Right Hand ◽  
Linear Differential

scholarly journals On Transformation and Oscillation of Linear Differential System

1977 ◽  
Vol 29 (2) ◽  
pp. 392-399 ◽  
Author(s):  
Donald F. St. Mary
Keyword(s):  
Differential System ◽  
Comparison Theorem ◽  
Linear Case ◽  
Linear Differential System ◽  
Oscillation Theorem ◽  
Differential Systems ◽  
Order Linear ◽  
Linear Differential Systems ◽  
Linear Differential ◽  
The Relationship

In this paper we study second order linear differential systems. We examine the relationship between oscillation of n-dimensional systems and certain associated n-dimensional systems, where m ≧ n. Several theorems are presented which unify and encompass in the linear case a number of results from the literature. In particular, we present a transformation which extends an oscillation theorem due to Allegretto and Erbe [1], and a comparison theorem due to Kreith [9], and explains some work of Howard [7].

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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