On a Comparison Theorem of Hille for Self-Adjoint Second Order Linear Differential Systems

1984 ◽  
Vol 15 (6) ◽  
pp. 1094-1099
Author(s):  
D. F. St. Mary
Keyword(s):  
Comparison Theorem ◽  
Second Order ◽  
Differential Systems ◽  
Order Linear ◽  
Linear Differential Systems ◽  
Linear Differential

scholarly journals On Transformation and Oscillation of Linear Differential System

1977 ◽  
Vol 29 (2) ◽  
pp. 392-399 ◽  
Author(s):  
Donald F. St. Mary
Keyword(s):  
Differential System ◽  
Comparison Theorem ◽  
Linear Case ◽  
Linear Differential System ◽  
Oscillation Theorem ◽  
Differential Systems ◽  
Order Linear ◽  
Linear Differential Systems ◽  
Linear Differential ◽  
The Relationship

In this paper we study second order linear differential systems. We examine the relationship between oscillation of n-dimensional systems and certain associated n-dimensional systems, where m ≧ n. Several theorems are presented which unify and encompass in the linear case a number of results from the literature. In particular, we present a transformation which extends an oscillation theorem due to Allegretto and Erbe [1], and a comparison theorem due to Kreith [9], and explains some work of Howard [7].

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