Necessary and Sufficient Conditions for the Oscillation of a Second Order Linear Differential Equation

2000 ◽  
Vol 213 (1) ◽  
pp. 105-115 ◽  
Author(s):  
M.R.S. Kulenović ◽  
Ć. Ljubović
Keyword(s):  
Differential Equation ◽  
Linear Differential Equation ◽  
Sufficient Conditions ◽  
Second Order ◽  
Necessary And Sufficient Conditions ◽  
Order Linear Differential Equation ◽  
Order Linear ◽  
Linear Differential ◽  
Necessary And Sufficient

On the influence of integral perturbations to the asymptotic stability of solutions of a second-order linear differential equation

2020 ◽  
Vol 17 (2) ◽  
pp. 188-195
Author(s):  
Samandar Iskandarov ◽  
Nazigai Abdiraiimova
Keyword(s):  
Differential Equation ◽  
Asymptotic Stability ◽  
Linear Differential Equation ◽  
Sufficient Conditions ◽  
Second Order ◽  
Order Linear Differential Equation ◽  
Stability Of Solutions ◽  
Volterra Type ◽  
Order Linear ◽  
Linear Differential

Sufficient conditions for the asymptotic stability of the solutions of a second-order linear integro-differential equation of the Volterra type are established in the case where the solutions of the corresponding second-order linear differential equation may have no property under study. Thus, the influence of integral perturbations on the asymptotic stability of solutions of linear differential equations of the second order is revealed. For this purpose, the method of auxiliary kernels is developed. An illustrative example is given.

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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