THE SOLVABILITY OF SOME KINDS OF SINGULAR INTEGRAL EQUATIONS OF CONVOLUTION TYPE WITH VARIABLE INTEGRAL LIMITS

Wenwen Zhang; Yanxin Lei; Pingrun Li

doi:10.11948/20230358

2024 Volume 14 Issue 4

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Article navigation > Journal of Applied Analysis & Computation > 2024 > 14(4): 2207-2227

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Wenwen Zhang, Yanxin Lei, Pingrun Li. THE SOLVABILITY OF SOME KINDS OF SINGULAR INTEGRAL EQUATIONS OF CONVOLUTION TYPE WITH VARIABLE INTEGRAL LIMITS[J]. Journal of Applied Analysis & Computation, 2024, 14(4): 2207-2227. doi: 10.11948/20230358

Citation:

Wenwen Zhang, Yanxin Lei, Pingrun Li. THE SOLVABILITY OF SOME KINDS OF SINGULAR INTEGRAL EQUATIONS OF CONVOLUTION TYPE WITH VARIABLE INTEGRAL LIMITS[J]. Journal of Applied Analysis & Computation, 2024, 14(4): 2207-2227. doi: 10.11948/20230358

THE SOLVABILITY OF SOME KINDS OF SINGULAR INTEGRAL EQUATIONS OF CONVOLUTION TYPE WITH VARIABLE INTEGRAL LIMITS

1.
School of Mathematical Sciences, Qufu Normal University, Qufu 273165, China

Author Bio: Email: z6483384940224@163.com(W. Zhang); Email: leiyanxin1228@163.com(Y. Lei)
Corresponding author: Email: lipingrun@163.com(P. Li)

Abstract

Abstract

In this paper, we discuss several classes of convolution type singular integral equations with variable integral limits in class $ H^*_1 $. By means of the theory of complex analysis, Fourier analysis and integral transforms, we can transform singular integral equations with variable integral limits into the Riemann boundary value problems with discontinuous coefficients. Under the solvability conditions, the existence and uniqueness of the general solutions can be obtained. Further, we analyze the asymptotic properties of the solutions at the nodes. Our work improves the Noether theory of singular integral equations and boundary value problems, and develops the knowledge architecture of complex analysis.
- Singular integral equations /
- variable integral limits /
- Riemann boundary value problems /
- Wiener-Hopf type /
- dual type /
- Fourier integral transform
MSC: 45E10, 30E25, 45E05

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References

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