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Holomorphic solutions and solvability theory for a class of linear complete singular integro-differential equations with convolution by Riemann–Hilbert method

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Abstract

In this article, we investigate a class of linear complete singular integro-differential equations of convolution type with Fredholm integral operator in the function class \(\{0\}\). To prove the existence of solution for the equations, we first propose the regularization method of complex integral equations, and then we establish the theory of Noether solvability. By using the relation between Cauchy type integral and Fourier integral, we transform such equations into the complete singular integral equations, and on this basis we transform further the obtained equations into boundary value problems of holomorphic functions with node (i.e., discontinuous coefficients). The holomorphic solution and conditions of solvability are obtained via the method of regularization. Our approach of solving equations is novel and effective, which is different from the classical method. Meanwhile, we also discuss the asymptotic stability of solutions. Therefore, this article has a great significance for the study of developing functional analysis, complex analysis, and differential-integral equations, also provides theoretical support for the study of engineering mechanics, elastic mechanics and mathematical Modeling.

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Acknowledgements

The authors are very grateful to the anonymous referees for their valuable suggestions and comments, which helped to improve the quality of the paper.

Funding

This work is supported financially by the National Natural Science Foundation of China (11971015).

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  1. School of Mathematical Science, Qufu Normal University, Qufu, 273165, People’s Republic of China

    Pingrun Li

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Li, P. Holomorphic solutions and solvability theory for a class of linear complete singular integro-differential equations with convolution by Riemann–Hilbert method. Anal.Math.Phys. 12, 146 (2022). https://doi.org/10.1007/s13324-022-00759-6

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  • DOI: https://doi.org/10.1007/s13324-022-00759-6

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