Integration of second order linear differential equation with mixed boundary conditions

1972 ◽  
Vol 3 (1-4) ◽  
pp. 389-397 ◽  
Author(s):  
Riaz A. Usmani
Keyword(s):  
Differential Equation ◽  
Boundary Conditions ◽  
Linear Differential Equation ◽  
Mixed Boundary ◽  
Mixed Boundary Conditions ◽  
Second Order ◽  
Order Linear Differential Equation ◽  
Order Linear ◽  
Linear Differential

scholarly journals The Distance between Points of a Solution of a Second Order Linear Differential Equation Satisfying General Boundary Conditions

2014 ◽  
Vol 2014 ◽  
pp. 1-17 ◽  
Author(s):  
Pedro Almenar ◽  
Lucas Jódar
Keyword(s):  
Differential Equation ◽  
Boundary Conditions ◽  
Linear Differential Equation ◽  
Minimum Distance ◽  
Second Order ◽  
Order Linear Differential Equation ◽  
Lower And Upper Bounds ◽  
Order Linear ◽  
Separated Boundary Conditions ◽  
Linear Differential

This paper presents a method to obtain lower and upper bounds for the minimum distance between pointsaandbof the solution of the second order linear differential equationy′′+q(x)y=0satisfying general separated boundary conditions of the typea11y(a)+a12y′(a)=0anda21y(b)+a22y′(b)=0. The method is based on the recursive application of a linear operator to certain functions, a recursive application that makes these bounds converge to the exact distance betweenaandbas the recursivity index grows. The method covers conjugacy and disfocality as particular cases.

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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