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.

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

A mechanical method for the solution of second-order linear differential equations

1931 ◽  
Vol 27 (4) ◽  
pp. 546-552 ◽  
Author(s):  
E. C. Bullard ◽  
P. B. Moon
Keyword(s):  
Differential Equation ◽  
Differential Equations ◽  
Boundary Conditions ◽  
Order Differential Equation ◽  
Second Order ◽  
Linear Differential Equations ◽  
Mechanical Method ◽  
Order Linear ◽  
Second Order Differential Equation ◽  
Linear Differential

A mechanical method of integrating a second-order differential equation, with any boundary conditions, is described and its applications are discussed.

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