The Leading Term of the Asymptotics of Solutions of Linear Differential Equations with First-Order Distribution Coefficients

2019 ◽  
Vol 106 (1-2) ◽  
pp. 81-88
Author(s):  
N. N. Konechnaya ◽  
K. A. Mirzoev
Keyword(s):  
Differential Equations ◽  
Distribution Coefficients ◽  
Linear Differential Equations ◽  
Asymptotics Of Solutions ◽  
First Order ◽  
Leading Term ◽  
Linear Differential

The Wave Theory of the Electron

1928 ◽  
Vol 24 (4) ◽  
pp. 501-505 ◽  
Author(s):  
J. M. Whittaker
Keyword(s):  
Wave Function ◽  
Differential Equations ◽  
Fourth Order ◽  
Commutative Algebra ◽  
Wave Theory ◽  
Wave Functions ◽  
Linear Differential Equations ◽  
Wave Mechanics ◽  
First Order ◽  
Linear Differential

In two recent papers Dirac has shown how the “duplexity” phenomena of the atom can be accounted for without recourse to the hypothesis of the spinning electron. The investigation is carried out by the methods of non-commutative algebra, the wave function ψ being a matrix of the fourth order. An alternative presentation of the theory, using the methods of wave mechanics, has been given by Darwin. The four-rowed matrix ψ is replaced by four wave functions ψ1, ψ2, ψ3, ψ4 satisfying four linear differential equations of the first order. These functions are related to one particular direction, and the work can only be given invariance of form at the expense of much additional complication, the four wave functions being replaced by sixteen.

scholarly journals On a Problem Arising in Application of the Re-Quantization Method to Construct Asymptotics of Solutions to Linear Differential Equations with Holomorphic Coefficients at Infinity

2019 ◽  
Vol 24 (1) ◽  
pp. 16 ◽  
Author(s):  
Maria Korovina ◽  
Ilya Smirnov ◽  
Vladimir Smirnov
Keyword(s):  
Differential Equations ◽  
Linear Differential Equations ◽  
Analytical Theory ◽  
Uniform Asymptotics ◽  
Quantization Method ◽  
Asymptotics Of Solutions ◽  
Borel Transform ◽  
Analysis Methods ◽  
Linear Differential ◽  
Resurgent Analysis

The re-quantization method—one of the resurgent analysis methods of current importance—is developed in this study. It is widely used in the analytical theory of linear differential equations. With the help of the re-quantization method, the problem of constructing the asymptotics of the inverse Laplace–Borel transform is solved for a particular type of functions with holomorphic coefficients that exponentially grow at zero. Two examples of constructing the uniform asymptotics at infinity for the second- and forth-order differential equations with the help of the re-quantization method and the result obtained in this study are considered.

On Asymptotics of Solutions to Some Linear Differential Equations

2019 ◽  
Vol 241 (5) ◽  
pp. 614-621
Author(s):  
K. A. Mirzoev ◽  
N. N. Konechnaya ◽  
T. A. Safonova ◽  
R. N. Tagirova
Keyword(s):  
Differential Equations ◽  
Linear Differential Equations ◽  
Asymptotics Of Solutions ◽  
Linear Differential

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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