Classification of second-order linear differential equations and an application to singular elliptic eigenvalue problems

2012 ◽  
Vol 44 (3) ◽  
pp. 545-562 ◽  
Author(s):  
Yūki Naito
Keyword(s):  
Differential Equations ◽  
Eigenvalue Problems ◽  
Second Order ◽  
Linear Differential Equations ◽  
Order Linear ◽  
Linear Differential ◽  
Elliptic Eigenvalue Problems

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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