Invertibility of first-order linear differential operators

1998 ◽  
Vol 64 (5) ◽  
pp. 688-693 ◽  
Author(s):  
M. K. Chernyshov
Keyword(s):  
Differential Operators ◽  
Order Linear ◽  
First Order ◽  
Linear Differential Operators ◽  
Linear Differential

The Oscillation of Fourth Order Linear Differential Operators

1975 ◽  
Vol 27 (1) ◽  
pp. 138-145 ◽  
Author(s):  
Roger T. Lewis
Keyword(s):  
Fourth Order ◽  
Differential Operators ◽  
Adjoint Operator ◽  
Oscillatory Behavior ◽  
The Self ◽  
Order Operator ◽  
Order Linear ◽  
Linear Differential Operators ◽  
Even Order ◽  
Linear Differential

Define the self-adjoint operatorwhere r(x) > 0 on (0, ∞) and q and p are real-valued. The coefficient q is assumed to be differentiate on (0, ∞) and r is assumed to be twice differentia t e on (0, ∞).The oscillatory behavior of L4 as well as the general even order operator has been considered by Leigh ton and Nehari [5], Glazman [2], Reid [7], Hinton [3], Barrett [1], Hunt and Namb∞diri [4], Schneider [8], and Lewis [6].

scholarly journals Ger-type and Hyers-Ulam stabilities for the first-order linear differential operators of entire functions

2004 ◽  
Vol 2004 (22) ◽  
pp. 1151-1158 ◽  
Author(s):  
Takeshi Miura ◽  
Go Hirasawa ◽  
Sin-Ei Takahasi
Keyword(s):  
Entire Function ◽  
Differential Operator ◽  
Stability Problem ◽  
Differential Operators ◽  
Entire Functions ◽  
Ulam Stability ◽  
Nonzero Constant ◽  
First Order ◽  
Linear Differential Operators ◽  
Linear Differential

Lethbe an entire function andTha differential operator defined byThf=f′+hf. We show thatThhas the Hyers-Ulam stability if and only ifhis a nonzero constant. We also consider Ger-type stability problem for|1−f′/hf|≤ϵ.

Sign in / Sign up

Export Citation Format

Share Document