Study of systems of Hammerstein integral equations of the first kind

Abstract

The article addresses systems of Hammerstein integral equations of the first kind, in which the determinant of the non-diagonal matrix-kernel is identically equal to zero.The class of problems under consideration has fundamental differences from standard cases: the solution may not exist, be non-unique, or depend on high derivatives of the input data. In terms of matrix pencils, sufficient conditions for the local existence of a unique solution in the class of continuous functions are formulated. Illustrative examples are given. Difficulties arising in the construction of numerical methods for solving these problems are discussed.

Bulatov M., Liang H., Solovarova L. (2025) "Study of systems of Hammerstein integral equations of the first kind " Dolomites Research Notes on Approximation, 18(2), 79-84. DOI: 10.25430/pupj-DRNA-2025-2-10  
Year of Publication
2025
Journal
Dolomites Research Notes on Approximation
Volume
18
Issue Number
2
Start Page
79
Last Page
84
Date Published
03/2025
ISSN Number
2035-6803
Serial Article Number
10
DOI
10.25430/pupj-DRNA-2025-2-10
Issue
Section
Articles