On the solvability of a class of Volterra operator equations of the first kind with piecewise continuous kernels

N. A. Sidorov; D. N. Sidorov

doi:10.1134/S0001434614110170

On the solvability of a class of Volterra operator equations of the first kind with piecewise continuous kernels

N. A. Sidorov^*
, D. N. Sidorov

^*Corresponding author for this work

Irkutsk State University
Melent'ev Institute of Power Engineering Systems
Irkutsk National Research Technical University

Research output: Contribution to journal › Article › peer-review

25 Scopus citations

Abstract

We obtain sufficient conditions for the existence and uniqueness of continuous solutions of Volterra operator equations of the first kind with piecewise determined kernels. For the case in which the solution is not unique, we prove existence theorems for the parametric families of solutions and present their asymptotics in the form of logarithmic polynomials.

Original language	English
Pages (from-to)	811-826
Number of pages	16
Journal	Mathematical Notes
Volume	96
Issue number	5-6
DOIs	https://doi.org/10.1134/S0001434614110170
State	Published - 2014
Externally published	Yes

Keywords

Banach space
Fredholm operator
Fredholm point
Jordan set
Volterra operator equation
asymptotic approximation
successive approximation method

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10.1134/S0001434614110170

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title = "On the solvability of a class of Volterra operator equations of the first kind with piecewise continuous kernels",

abstract = "We obtain sufficient conditions for the existence and uniqueness of continuous solutions of Volterra operator equations of the first kind with piecewise determined kernels. For the case in which the solution is not unique, we prove existence theorems for the parametric families of solutions and present their asymptotics in the form of logarithmic polynomials.",

keywords = "Banach space, Fredholm operator, Fredholm point, Jordan set, Volterra operator equation, asymptotic approximation, successive approximation method",

author = "Sidorov, \{N. A.\} and Sidorov, \{D. N.\}",

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year = "2014",

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T1 - On the solvability of a class of Volterra operator equations of the first kind with piecewise continuous kernels

AU - Sidorov, N. A.

AU - Sidorov, D. N.

PY - 2014

Y1 - 2014

N2 - We obtain sufficient conditions for the existence and uniqueness of continuous solutions of Volterra operator equations of the first kind with piecewise determined kernels. For the case in which the solution is not unique, we prove existence theorems for the parametric families of solutions and present their asymptotics in the form of logarithmic polynomials.

AB - We obtain sufficient conditions for the existence and uniqueness of continuous solutions of Volterra operator equations of the first kind with piecewise determined kernels. For the case in which the solution is not unique, we prove existence theorems for the parametric families of solutions and present their asymptotics in the form of logarithmic polynomials.

KW - Banach space

KW - Fredholm operator

KW - Fredholm point

KW - Jordan set

KW - Volterra operator equation

KW - asymptotic approximation

KW - successive approximation method

UR - https://www.scopus.com/pages/publications/84919904318

U2 - 10.1134/S0001434614110170

DO - 10.1134/S0001434614110170

M3 - 文章

AN - SCOPUS:84919904318

SN - 0001-4346

VL - 96

SP - 811

EP - 826

JO - Mathematical Notes

JF - Mathematical Notes

IS - 5-6

ER -

On the solvability of a class of Volterra operator equations of the first kind with piecewise continuous kernels

Abstract

Keywords

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