scholarly journals A characterization of Hyers–Ulam stability of first order linear differential operators

2003 ◽  
Vol 286 (1) ◽  
pp. 136-146 ◽  
Author(s):  
Takeshi Miura ◽  
Shizuo Miyajima ◽  
Sin-Ei Takahasi
Keyword(s):  
Differential Operators ◽  
Ulam Stability ◽  
Order Linear ◽  
First Order ◽  
Linear Differential Operators ◽  
Linear Differential

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.

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 Hyers-Ulam Stability of the First-Order Matrix Differential Equations

2015 ◽  
Vol 2015 ◽  
pp. 1-7
Author(s):  
Soon-Mo Jung
Keyword(s):  
Differential Equations ◽  
Variable Coefficients ◽  
Linear Differential Equations ◽  
Ulam Stability ◽  
Order Linear ◽  
First Order ◽  
Matrix Differential Equations ◽  
Homogeneous Matrix ◽  
Linear Differential ◽  
Matrix Differential

We prove the generalized Hyers-Ulam stability of the first-order linear homogeneous matrix differential equationsy→'(t)=A(t)y→(t). Moreover, we apply this result to prove the generalized Hyers-Ulam stability of thenth order linear differential equations with variable coefficients.

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