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This article is cited in 6 scientific papers (total in 6 papers)
MATHEMATICS
Construction of an analog of the Fredholm theorem for a class of model first order integro-differential equations with a singular point in the kernel
S. K. Zaripov Tajik National University, Republic of Tajikistan
Abstract:
In this work, integral representations of the manifold of solutions in terms of two arbitrary
constants have been found for a model first order integro-differential equation with a singular
point in the kernel. Although the kernel of this equation is not of the Fredholm type, the solution
of this equation in the class of functions vanishing at $x=a$ has been found in an explicit form. It
has been shown that the solution of the equation contains either two arbitrary constants or one
arbitrary constant. Moreover, the case where the integro-differential equation has a unique
solution has been revealed.
For the integro-differential equation, analogs of the Fredholm theorem have been constructed.
The existence of arbitrary constants in the general solution gives us chance to investigate
some initial or boundary value problems for this equation. However, it is necessary to note that, in
contrast to usual problems, these problems in our case are posed with different weights.
Correctness of the obtained results is verified with the help of detailed solutions of examples.
The method can be used for solving higher order model and non-model integro-differential
equations with singular and supersingular kernels.
Keywords:
model integro-differential equation, boundary singular points, manifold of solutions, integral representation, integral equation, characteristic equation.
Received: 08.12.2016
Citation:
S. K. Zaripov, “Construction of an analog of the Fredholm theorem for a class of model first order integro-differential equations with a singular point in the kernel”, Vestn. Tomsk. Gos. Univ. Mat. Mekh., 2017, no. 46, 24–35
Linking options:
https://www.mathnet.ru/eng/vtgu575 https://www.mathnet.ru/eng/vtgu/y2017/i46/p24
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Abstract page: | 195 | Full-text PDF : | 45 | References: | 35 |
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