求积分-微分方程边值问题唯一可解性的一种方法

Q A Iasaýı atyndaǵy Halyqaralyq qazaq-túrіk ýnıversıtetіnіń habarlary (fızıka matematıka ınformatıka serııasy) Pub Date : 2022-03-15 DOI:10.47526/2022-2/2524-0080.04

K. Nazarova

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引用次数: 0

摘要

利用改进的参数化方法研究了一类退化核线性Fredholm积分微分方程。利用基本矩阵，建立了具有退化核的Fredholm积分-微分方程的特殊Cauchy问题解的存在性条件。根据引入的附加参数，构造了一个线性代数方程组。给出了一类退化核Fredholm积分微分方程线性边值问题唯一可解的条件。

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ON ONE METHOD FOR OBTAINING UNIQUE SOLVABILITY OF A BOUNDARY VALUE PROBLEM FOR AN INTEGRO-DIFFERENTIAL EQUATION

The modified method of parametrization is used to study a linear Fredholm integro-differential equation with a degenerate kernel. Using the fundamental matrix, the conditions are established for the existence of a solution to the special Cauchy problem for the Fredholm integro-differential equation with a degenerate kernel. A system of linear algebraic equations is constructed with respect to the introduced additional parameters. Conditions for the unique solvability of a linear boundary value problem for the Fredholm integro-differential equation with a degenerate kernel are obtained.

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Q A Iasaýı atyndaǵy Halyqaralyq qazaq-túrіk ýnıversıtetіnіń habarlary (fızıka matematıka ınformatıka serııasy)

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