On the spectrum of Volterra integral equation with the "incompressible" kernel

被引：11

作者：

Amangaliyeva, Meiramkul M. ^{[1
]}

Jenaliyev, Muvasharkhan T. ^{[1
]}

Kosmakova, Minzilya T. ^{[1
]}

Ramazanov, Murat I. ^{[1
]}

机构：

[1] Inst Math Modelling, Alma Ata 050010, Kazakhstan

来源：

INTERNATIONAL CONFERENCE ON ANALYSIS AND APPLIED MATHEMATICS (ICAAM 2014) | 2014年 / 1611卷

关键词：

Singular Volterra integral equation; Spectrum; Incompressible kernel; Eigenfunction; Abel equation;

D O I：

10.1063/1.4893816

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

The article addresses the singular Volterra integral equation of the second kind which has the "incompressible" kernel. It is shown that the corresponding homogeneous equation for vertical bar lambda vertical bar > 1 has a continuous spectrum, and the multiplicity of the characteristic numbers grows with increasing vertical bar lambda vertical bar. The equation is reduced to Abel equation by using the regularization method. The eigenfunctions of the equation are found in an explicit form. We prove the solvability theorem of the nonhomogeneous equation in a case when the right-hand side of the equation belongs to a certain class.

引用

页码：127 / 132

页数：6