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Эта публикация цитируется в 1 научной статье (всего в 1 статье)
The linear Fredholm integral equations with functionals and parameters
L. R. Dreglea Sidorova, N. Sidorovb, D. Sidorovc a Department of Mechanics and Mathematics, Moscow State University, 1 Leninskie Gory., Moscow 119991, Russian Federation
b Institute of Mathematics and Information Technologies, Irkutsk State University, 1 K. Marx Str. Irkutsk 664025, Russian Federation
c Industrial Mathematics Laboratory, Baikal School of BRICS, Irkutsk National Research Technical University, Lermontov Str. 83, Irkutsk 664074, Russian Federation
Аннотация:
The theory of linear Fredholm integral-functional equations of the second kind with linear functionals and a parameter is considered. The necessary and sufficient conditions are obtained for the coefficients of the equation and those parameter values in the neighbourhood of which the equation has solutions. The leading terms of the asymptotics of the solutions are constructed. The constructive method is proposed for constructing a solution both in the regular case and in the irregular one. In the regular case, the solution is constructed as a Taylor series in powers of the parameter. In the irregular case, the solution is constructed as a Laurent series in powers of the parameter. The example is used to illustrate the proposed constructive theory and method.
Ключевые слова и фразы:
loaded equations, Fredholm equation, asymptotics, holomorphic solution.
Поступила в редакцию: 12.07.2023
Образец цитирования:
L. R. Dreglea Sidorov, N. Sidorov, D. Sidorov, “The linear Fredholm integral equations with functionals and parameters”, Bul. Acad. Ştiinţe Repub. Mold. Mat., 2023, № 2, 83–91
Образцы ссылок на эту страницу:
https://www.mathnet.ru/rus/basm594 https://www.mathnet.ru/rus/basm/y2023/i2/p83
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