Abstract
Using a modification of the approach previously developed by the authors, we show that finding solutions of one class of systems of linear Fredholm integral equations of the third kind on the real line with finitely many multipoint singularities is equivalent to finding solutions of a system of linear Fredholm integral equations of the second kind on the real line with additional conditions imposed on the kernels and the free term. The existence, nonexistence, uniqueness, and nonuniqueness of solutions of systems in this class are studied.
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Notes
A number \(\mu \) is called [1, p. 71] a characteristic value of the kernel \(k(x,y)\) if the homogeneous integral equation \(u(x)-\mu \int _{-\infty }^{\infty }k(x,y)u(x)dy=0 \) has nontrivial solutions. The nontrivial solutions of this homogeneous equation are called the eigenfunctions of the kernel corresponding to the characteristic value \(\mu \).
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Translated by V. Potapchouck
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Asanov, A., Asanov, R.A. One Class of Systems of Linear Fredholm Integral Equations of the Third Kind on the Real Line with Multipoint Singularities. Diff Equat 56, 1363–1370 (2020). https://doi.org/10.1134/S00122661200100122
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DOI: https://doi.org/10.1134/S00122661200100122