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Asymptotic Behavior of Solutions of Integral Equations with Homogeneous Kernels

Author

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  • Oleg Avsyankin

    (Institute of Mathematics, Mechanics and Computer Sciences, Regional Mathematical Center, Southern Federal University, Mil’chakova St., 8a, 344090 Rostov-on-Don, Russia)

Abstract

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.

Suggested Citation

  • Oleg Avsyankin, 2022. "Asymptotic Behavior of Solutions of Integral Equations with Homogeneous Kernels," Mathematics, MDPI, vol. 10(2), pages 1-11, January.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:2:p:180-:d:719643
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