The kth Conjugate Point Function for an Even Order Linear Differential Equation

1974 ◽  
Vol 42 (2) ◽  
pp. 563
Author(s):  
George W. Johnson
Keyword(s):  
Differential Equation ◽  
Linear Differential Equation ◽  
Conjugate Point ◽  
Order Linear Differential Equation ◽  
Point Function ◽  
Order Linear ◽  
Even Order ◽  
Linear Differential

On a Relation Between a Theorem of Hartman and a Theorem of Sherman

1973 ◽  
Vol 16 (2) ◽  
pp. 275-281 ◽  
Author(s):  
A. C. Peterson
Keyword(s):  
Differential Equation ◽  
Differential Equations ◽  
Linear Differential Equation ◽  
General Result ◽  
Nonlinear Differential Equations ◽  
Conjugate Point ◽  
Order Linear Differential Equation ◽  
Order Linear ◽  
Linear Differential ◽  
Image Position

We are concerned with the nth-order linear differential equation1where the coefficients are assumed to be continuous. Hartman [1] proved that (see Definition 2) the first conjugate point η1(t) of t satisfies2Hartman actually proved a more general result which has very important applications in nonlinear differential equations.

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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