Date Log
SOLVABILITY OF THE SINGULAR INTEGRAL EQUATION WITH ANALYTIC KERNELS AND ROTATIONS
Corresponding Author(s) : Phan Duc Tuan
UED Journal of Social Sciences, Humanities and Education,
Vol. 6 No. 2 (2016): UED JOURNAL OF SOCIAL SCIENCES, HUMANITIES AND EDUCATION
Abstract
In this paper we study the solvability and solution formula of singular integral equations with analytic kernels that shift in the case of a coefficient vanishing on the unit circle. In order to obtain such results, we first build the orthographic projection, thereby transfering these singular integral equations into the Cauchy singular integral equations without shifting. Then, based on the results of the Riemann boundary value problems, we indicate the sufficient conditions for existence of solutions and explicit solution formula of the original equation.
Keywords
Download Citation
Endnote/Zotero/Mendeley (RIS)BibTeX
-
[1] L. P. Castro, E. M. Rojas, S. Saitoh, N. M. Tuan and P. D. Tuan (2015), Solvability of singular integral equations with rotations and degenerate kernels in the vanishing coefficient case, Analysis and Applications, Vol.13, No.1, pp.1–21.
[2] L. H. Chuan, N. M. Tuan (2003), On the singular integral equations with Carleman shift in the case of the vanishing coefficien, Acta Mathematica Vietnamica, V. 28, N. 3, pp. 319-333.
[3] Gakhov F. D. (1966), Boundary value problems, Oxford.
[4] N. V. Mau (1989), On the solvability in closed form of the class of the complete singular integral equations, Diff. Equation, USSR, T. 25, N. 2, pp. 307-311.
[5] N. V. Mau, N. M. Tuan (1996), On solutions of integral equations with analytic kernels and rotations, Annales Polonici Mathematici, LXIII. 3, pp. 293-300.
[6] N. M. Tuan (1996), On a class of singular integral equations with rotations, Acta Mathematica Vietnamica, V. 21, N. 2, pp. 201-211.
[7] N. M. Tuan (1996), On solvability of a class of singular integral equations with rotation, Vietnam Journal of Mathematic, V. 24, N. 4, pp. 390-397.