Comparison Theorems for Eigenvalue Problems for nth Order Differential Equations

1988 ◽  
Vol 104 (4) ◽  
pp. 1204 ◽  
Author(s):  
Darrel Hankerson ◽  
Allan Peterson
Keyword(s):  
Differential Equations ◽  
Eigenvalue Problems ◽  
Comparison Theorems

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

scholarly journals Comparison theorems for fourth order differential equations

1986 ◽  
Vol 9 (1) ◽  
pp. 105-109
Author(s):  
Garret J. Etgen ◽  
Willie E. Taylor
Keyword(s):  
Continuous Function ◽  
Differential Equations ◽  
Fourth Order ◽  
Linear Equations ◽  
Oscillation Criterion ◽  
Comparison Theorems ◽  
Positive Continuous Function ◽  
Order Linear ◽  
All Solutions

This paper establishes an apparently overlooked relationship between the pair of fourth order linear equationsyiv−p(x)y=0andyiv+p(x)y=0, wherepis a positive, continuous function defined on[0,∞). It is shown that if all solutions of the first equation are nonoscillatory, then all solutions of the second equation must be nonoscillatory as well. An oscillation criterion for these equations is also given.

Comparison theorems for self-adjoint linear Hamiltonian eigenvalue problems

2013 ◽  
Vol 287 (5-6) ◽  
pp. 704-716 ◽  
Author(s):  
Roman Šimon Hilscher
Keyword(s):  
Eigenvalue Problems ◽  
Comparison Theorems

scholarly journals Comparison Theorems for the Multidimensional BDSDEs and Applications

2012 ◽  
Vol 2012 ◽  
pp. 1-14 ◽  
Author(s):  
Bo Zhu ◽  
Baoyan Han
Keyword(s):  
Differential Equations ◽  
Stochastic Differential Equations ◽  
Comparison Theorem ◽  
Existence Of Solutions ◽  
Minimal Solution ◽  
Comparison Theorems ◽  
Doubly Stochastic

A class of backward doubly stochastic differential equations (BDSDEs) are studied. We obtain a comparison theorem of these multidimensional BDSDEs. As its applications, we derive the existence of solutions for this multidimensional BDSDEs with continuous coefficients. We can also prove that this solution is the minimal solution of the BDSDE.

Sign in / Sign up

Export Citation Format

Share Document