xistence of Solutions for Volterra Singular Integral Equations in the Class of Exponentially Increasing Functions

ZHANG Wen-wen, LI Ping-run

doi:10.13371/j.cnki.chin.q.j.m.2025.02.002

Chinese Quarterly Journal of Mathematics >

2025 , Vol. 40 >Issue 2: 135 - 147

DOI: https://doi.org/10.13371/j.cnki.chin.q.j.m.2025.02.002

xistence of Solutions for Volterra Singular Integral Equations in the Class of Exponentially Increasing Functions

Expand

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

ZHANG Wen-wen (2000-), female, native of Weifang, Shandong, graduate student of Qufu Normal University, under postgraduate, engages in the boundary value problem of analytic function and singular integral equation; LI Ping-run (1966-), male, native of Yanzhou, Shandong, professor of Qufu Normal University, Ph.D., engages in the boundary value problem of analytic function, singular integral equation and Clifford analysis.

Received date: 2024-06-20

Online published: 2025-06-30

Supported by

Supported by National Natural Science Foundation of China (Grant No. 11971015)

Fold

Abstract

The goal of this paper is to investigate the theory of Noether solvability for Volterra singular integral equations (VSIEs) with convolution and Cauchy kernels in a more general function class. To obtain the analytic solutions, we transform such equations into boundary value problems with discontinuous coefficients by the properties of Fourier analysis. In view of the analytical Riemann-Hilbert method, the generalized Liouville theorem and Sokhotski-Plemelj formula, we get the uniqueness and existence of solutions for such problems, and study the asymptotic property of solutions at nodes. Therefore, this paper improves the theory of singular integral equations and boundary value problems.

Key words： Volterra singular integral equations; The theory of Noether solvability; The class of exponentially increasing functions; Riemann-Hilbert method

Cite this article

ZHANG Wen-wen, LI Ping-run . xistence of Solutions for Volterra Singular Integral Equations in the Class of Exponentially Increasing Functions[J]. Chinese Quarterly Journal of Mathematics, 2025 , 40(2) : 135 -147 . DOI: 10.13371/j.cnki.chin.q.j.m.2025.02.002

Options

Outlines

模态框（Modal）标题

Abstract

Cite this article