Linear Integral Equations of the Third Kind

1973 ◽  
Vol 4 (4) ◽  
pp. 609-622 ◽  
Author(s):  
G. R. Bart ◽  
R. L. Warnock
Keyword(s):  
Integral Equations ◽  
The Third ◽  
Linear Integral ◽  
Linear Integral Equations

scholarly journals Uniqueness of the Fredholm-Stiltjes Linear Integral Equations Solutions of the Third Kind

2021 ◽  
Vol 11 (04) ◽  
pp. 109-116
Author(s):  
Aizat Toigonbaeva ◽  
Avyt Asanov ◽  
Aisalkyn Kambarova ◽  
Gumushai Obodoeva ◽  
Ularbek Moldoyarov ◽  
...  
Keyword(s):  
Integral Equations ◽  
The Third ◽  
Linear Integral ◽  
Linear Integral Equations

scholarly journals On Solvability Conditions for a Certain Conjugation Problem

Axioms ◽  
2021 ◽  
Vol 10 (3) ◽  
pp. 234
Author(s):  
Vladimir Vasilyev ◽  
Nikolai Eberlein
Keyword(s):  
General Solution ◽  
Differential Equations ◽  
Integral Equations ◽  
Mellin Transform ◽  
Algebraic Equations ◽  
Conjugation Problem ◽  
Solvability Conditions ◽  
Linear Algebraic Equations ◽  
Linear Integral ◽  
Linear Integral Equations

We study a certain conjugation problem for a pair of elliptic pseudo-differential equations with homogeneous symbols inside and outside of a plane sector. The solution is sought in corresponding Sobolev–Slobodetskii spaces. Using the wave factorization concept for elliptic symbols, we derive a general solution of the conjugation problem. Adding some complementary conditions, we obtain a system of linear integral equations. If the symbols are homogeneous, then we can apply the Mellin transform to such a system to reduce it to a system of linear algebraic equations with respect to unknown functions.

On the location of the Weyl circles

1981 ◽  
Vol 88 (3-4) ◽  
pp. 345-356 ◽  
Author(s):  
F. V. Atkinson
Keyword(s):  
Integral Equations ◽  
Complex Plane ◽  
Riccati Equations ◽  
Sturm Liouville ◽  
Linear Integral ◽  
Linear Integral Equations

SynopsisThe paper deals with explicit estimates concerning certain circles in the complex plane which were associated with Sturm–Liouville problems by H. Weyl. By the use of Riccati equations instead of linear integral equations, improvements are obtained for results of Everitt and Halvorsen concerning the behaviour of the Titchmarsh–Weyl m-coefficient.

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