Singularly perturbed integro-differential equations with degenerate Hammerstein's kernel

被引：0

作者：

Bobodzhanova, M. A. ^{[1
]}

Kalimbetov, B. T. ^{[2
]}

Safonov, V. F. ^{[1
]}

机构：

[1] Natl Res Univ MPEI, Moscow, Russia

[2] A Kuatbekov PeoplesFriendship Univ, Shymkent, Kazakhstan

来源：

BULLETIN OF THE KARAGANDA UNIVERSITY-MATHEMATICS SERIES | 2024年 / 116卷 / 04期

基金：

俄罗斯科学基金会;

关键词：

singularly perturbed; Hammerstein's equation; degenerate kernel; Fredholm's equations; analytic function; Laurent's series; passage to the limit; the Maple program; RAPIDLY OSCILLATING COEFFICIENTS; DIFFERENTIAL-EQUATIONS; REGULARIZATION METHOD; ASYMPTOTIC SOLUTIONS; SYSTEMS;

D O I：

10.31489/2024M4/57-68

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Singularly perturbed integro-differential equations with degenerate kernels are considered. It is shown that in the linear case these problems are always uniquely solvable with continuous coefficients, while nonlinear problems either have no real solutions at all or have several of them. For linear problems, the results of Bobojanova are refined; in particular, necessary and sufficient conditions are given for the existence of a finite limit of their solutions as the small parameter tends to zero and sufficient conditions under which the passage to the limit to the solution of the degenerate equation is possible.

引用

页码：57 / 68

页数：12

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