Solution of multidimensional integral equations of the first kind with a potential type kernel

2001 ◽  
pp. 249-288
Keyword(s):  
Integral Equations ◽  
Potential Type ◽  
Multidimensional Integral

scholarly journals Asymptotic Behavior of Solutions of Integral Equations with Homogeneous Kernels

Mathematics ◽  
2022 ◽  
Vol 10 (2) ◽  
pp. 180
Author(s):  
Oleg Avsyankin
Keyword(s):  
Integral Equation ◽  
Asymptotic Behavior ◽  
Integral Equations ◽  
Spherical Harmonics ◽  
Special Class ◽  
Continuous Functions ◽  
Asymptotic Behavior Of Solutions ◽  
Free Term ◽  
Research Technique ◽  
Multidimensional Integral

The multidimensional integral equation of second kind with a homogeneous of degree (−n) kernel is considered. The special class of continuous functions with a given asymptotic behavior in the neighborhood of zero is defined. It is proved that, if the free term of the integral equation belongs to this class and the equation itself is solvable, then its solution also belongs to this class. To solve this problem, a special research technique is used. The above-mentioned technique is based on the decomposition of both the solution and the free term in spherical harmonics.

Regularization of Multidimensional Integral Equations of the 1st Kind in Variable Exponent Spaces

2010 ◽  
Author(s):  
Stefan Samko ◽  
Salaudin Umarkhadzhiev ◽  
Theodore E. Simos ◽  
George Psihoyios ◽  
Ch. Tsitouras
Keyword(s):  
Integral Equations ◽  
Variable Exponent ◽  
Variable Exponent Spaces ◽  
Multidimensional Integral

scholarly journals Nonlinear integral equations with potential type kernels on a semiaxis

2013 ◽  
Author(s):  
С.Н. Асхабов
Keyword(s):  
Integral Equations ◽  
Nonlinear Integral Equations ◽  
Potential Type

Методом монотонных операторов в комплексных пространствах Лебега доказываются теоремы о существовании, единственности и способах нахождения решения для различных классов нелинейных интегральных уравнений с ядрами типа потенциала. Получены оценки норм решений и скорости сходимости к ним последовательных приближений пикаровского типа.

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