Oscillation and Comparison Theorems for Second Order Linear Differential Equations with Integrable Coefficients

1974 ◽  
Vol 26 (02) ◽  
pp. 294-301
Author(s):  
G. Butler ◽  
J. W. Macki
Keyword(s):  
Differential Equations ◽  
Eigenvalue Problems ◽  
Second Order ◽  
Linear Differential Equations ◽  
Comparison Theorems ◽  
Standard Theory ◽  
General Hypothesis ◽  
Order Linear ◽  
Linear Differential ◽  
Image Position

The classical comparison and interlacing theorems of Sturm were originally proved for the equations under the assumption that all coefficients are real-valued, continuous, and p > 0, P > 0. Atkinson [1, Chapter 8] has carried out the standard theory for eigenvalue problems involving (1), under the more general hypothesis

An Improved Wintner Oscillation Criterion for Second Order Linear Differential Equations

1984 ◽  
Vol 27 (1) ◽  
pp. 117-121
Author(s):  
George W. Johnson ◽  
Jurang Yan
Keyword(s):  
Differential Equations ◽  
Second Order ◽  
Oscillation Criterion ◽  
Linear Differential Equations ◽  
Iterative Technique ◽  
Oscillation Theorem ◽  
Order Linear ◽  
Linear Differential ◽  
Image Position

AbstractAn iterative technique is used to establish an oscillation theorem for the equation x″+ a(t)x=0 which relaxes the condition that a(t) satisfywithout the restriction that

Oscillation on Finite or Infinite Intervals of Second Order Linear Differential Equations(1)

1971 ◽  
Vol 14 (4) ◽  
pp. 539-550 ◽  
Author(s):  
D. Willett
Keyword(s):  
Differential Equations ◽  
Second Order ◽  
Linear Differential Equations ◽  
Riccati Transformation ◽  
Order Linear ◽  
Infinite Intervals ◽  
Linear Differential ◽  
Image Position

Recently, Ronveaux [11] has shown how to use a combination of a Riccati transformation and a homographie transformation to estimate both from below and above the distance between a zero and the succeeding or preceding extremum (zero of y' ) of solutions of1.1In this paper, we show how such transformations can be used to derive an equation from which the distance between successive zeros of a solution y of (1.1) can be estimated directly.

scholarly journals Comparison theorems of Hille-Wintner type for third order linear differential equations

1980 ◽  
Vol 21 (2) ◽  
pp. 175-188 ◽  
Author(s):  
L. Erbe
Keyword(s):  
Differential Equations ◽  
Linear Equation ◽  
Linear Equations ◽  
Second Order ◽  
Linear Differential Equations ◽  
Comparison Theorems ◽  
Third Order ◽  
Order Linear ◽  
The Third ◽  
Linear Differential

Integral comparison theorems of Hille-Wintner type of second order linear equations are shown to be valid for the third order linear equation y‴ + q(t)y = 0.

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