Open AccessTHE EXISTENCE OF A FINITE-DIMENSIONAL SOLUTION NONLINEAR INTEGRAL FREDHOLM EQUATION OF THE FIRST KIND
Author(s) -
A. Saadabaev,
A.R. Abdyldaeva
Publication year - 2020
Publication title -
vestnik kyrgyzskogo gosudarstvennogo universiteta stroitelʹstva, transporta i arhitektury im.n.isanova/n.isanov atyndagy kyrgyz mamlekettik kuruluš,transport žana arhitektura universitetinin žarčysy
Language(s) - English
Resource type - Journals
eISSN - 1694-8181
pISSN - 1694-5298
DOI - 10.35803/1694-5298.2020.3.459-466
Subject(s) - fredholm integral equation , mathematics , integral equation , mathematical analysis , parametrix , operator (biology) , kernel (algebra) , nonlinear system , partial differential equation , fredholm theory , function (biology) , fourier integral operator , pure mathematics , physics , biochemistry , chemistry , repressor , quantum mechanics , evolutionary biology , biology , transcription factor , gene
In this paper, the existence of a finite-dimensional solution of a nonlinear integral equation is proved when the right-hand side and the kernel are given approximately. A finite-dimensional regularizing operator is constructed, and it is proved that for n → ∞ and for a special choice of the parameter n from δ, the solution of the finite-dimensional problem converges to the exact solution of the original equation. It is shown by an example that using the Green's function it is possible to approximate a differential operator by an integral operator.