Reduction of an n-th Order Linear Differential Equation and m-Point Boundary Conditions to an Equivalent Matrix System

1946 ◽  
Vol 68 (1) ◽  
pp. 179 ◽  
Author(s):  
Randal H. Cole
Keyword(s):  
Differential Equation ◽  
Boundary Conditions ◽  
Linear Differential Equation ◽  
Matrix System ◽  
Order Linear Differential Equation ◽  
Point Boundary ◽  
Order Linear ◽  
Linear Differential

Lower bounds for the spectrum of a second order linear differential equation with a coefficient whose negative part is p-integrable

1984 ◽  
Vol 97 ◽  
pp. 105-107
Author(s):  
B. J. Harris
Keyword(s):  
Differential Equation ◽  
Boundary Conditions ◽  
Linear Differential Equation ◽  
Differential Expression ◽  
Lower Bounds ◽  
Linear Operators ◽  
Order Linear Differential Equation ◽  
Negative Part ◽  
Order Linear ◽  
Linear Differential

SynopsisWe consider ihe differential expression M[y]: = −y″ + qy on [0, ∞) where q_∈ Lp [0, ∞) for some p ≧ 1. It is known that M, together with the boundary conditions y(0) = 0 or y′(0) = 0, defines linear operators on L2 [0, ∞). We obtain lower bounds for the spectra of these operators. Our bounds depend on the Lp norm of q_ and extend results of Everitt and Veling.

On the Ordering of Multi-Point Boundary Value Functions

1970 ◽  
Vol 13 (4) ◽  
pp. 507-513 ◽  
Author(s):  
A. C. Peterson
Keyword(s):  
Differential Equation ◽  
Linear Differential Equation ◽  
Boundary Value ◽  
Value Functions ◽  
Order Linear Differential Equation ◽  
Point Boundary ◽  
Order Linear ◽  
Linear Differential ◽  
Image Position

We are concerned with the nth-order linear differential equation1where the coefficients are continuous. Aliev [1, 2] showed, in papers unavailable to the author that for n = 4(see Definition 2). Theorems 1 and 5 give respectively nth-order generalizations of these two results.

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

scholarly journals A Comparison between the fourth order linear differential equation with its boundary value problem

2020 ◽  
Vol 99 (3) ◽  
pp. 18-25
Author(s):  
Karwan H.F. Jwamer ◽  
◽  
Rando R.Q. Rasul ◽  
Keyword(s):  
Differential Equation ◽  
Boundary Value Problem ◽  
Linear Differential Equation ◽  
Fourth Order ◽  
Upper Bound ◽  
Boundary Value ◽  
Order Linear Differential Equation ◽  
Order Linear ◽  
Linear Differential

In this paper, we study a fourth order linear differential equation. We found an upper bound for the solutions of this differential equation and also, we prove that all the solutions are in L4(0, ∞). By comparing these results we obtain that all the eigenfunction of the boundary value problem generated by this differential equation are bounded and in L4(0, ∞).

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