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The linear Fredholm integral equations with functionals and parameters
Authors: L. R. Dreglea Sidorov, N. Sidorov and D. Sidorov
Keywords: loaded equations, Fredholm equation, asymptotics, holomorphic solution
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Keywords: loaded equations, Fredholm equation, asymptotics, holomorphic solution
Abstract
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.L. R. Dreglea Sidorov
Department of Mechanics and Mathematics, Moscow State
University, 1 Leninskie Gory., Moscow 119991, Russian
Federation
E-mail:
N. Sidorov
Institute of Mathematics and Information Technologies,
Irkutsk State University, 1 K. Marx Str. Irkutsk 664025,
Russian Federation
E-mail:
D. Sidorov
Industrial Mathematics Laboratory, Baikal School of
BRICS, Irkutsk National Research Technical University,
Lermontov Str. 83, Irkutsk 664074, Russian Federation
E-mail: ,
Department of Mechanics and Mathematics, Moscow State
University, 1 Leninskie Gory., Moscow 119991, Russian
Federation
E-mail:
N. Sidorov
Institute of Mathematics and Information Technologies,
Irkutsk State University, 1 K. Marx Str. Irkutsk 664025,
Russian Federation
E-mail:
D. Sidorov
Industrial Mathematics Laboratory, Baikal School of
BRICS, Irkutsk National Research Technical University,
Lermontov Str. 83, Irkutsk 664074, Russian Federation
E-mail: ,
DOI
https://doi.org/10.56415/basm.y2023.i2.p83Fulltext
– 0.12 Mb
Contents
- The Second Hankel Determinant for k-symmetrical Functions
- Relative Separation Axioms via Semi-Open Sets
- Growth Properties of Solutions to Higher Order Complex Linear Differential Equations with Analytic Coefficients in the Annulus
- On T-nilpotence of a matrix set
- On the Existence of Stationary Nash Equilibria for Mean Payoff Games on Graphs
- Global Asymptotic Stability of Generalized Homogeneous Dynamical Systems
- The linear Fredholm integral equations with functionals and parameters
- B-spline collocation method for solving Fredholm integral equations with discontinuous right-hand side
- On recursive 1-differentiability of the quasigroup prolongations
- Zero-Order Markov Processes with Multiple Final Sequences of States
