Existence of solutions for Volterra singular integral equations in the class of differentiable functions

Wenwen Zhang and Pingrun Li

Applied Mathematics and Computation, 2025, vol. 500, issue C

Abstract: In this paper, our purpose is to obtain the general solutions of several kinds of Volterra singular integral equations (VSIEs) in the class of differentiable functions. By constructing some operators and using the properties of integral transforms and conformal mappings, we transform VSIEs in the class of differentiable functions into the Riemann-Hilbert problems with discontinuity on a circle. By means of the principle of analytic continuation and Sokhotski-Plemelj formula, we obtain solutions of Riemann-Hilbert problems in the case of non-normal type, and further discuss the asymptotic properties of the solutions at the nodes.

Keywords: Volterra singular integral equations; Theory of Noetherian solvability; The class of differentiable functions; Discontinuous property; Boundary value problems (search for similar items in EconPapers)
Date: 2025
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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:500:y:2025:i:c:s0096300325001754

DOI: 10.1016/j.amc.2025.129448

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