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Bykov, Y.V. (1981) On Some Problems in the Theory of Integro-Differential Equations.

has been cited by the following article:

• TITLE: Solvability and Construction of a Solution to the Fredholm Integral Equation of the First Kind

  AUTHORS: Aisagaliev Serikbai, Nurmagambetov Dias, Sevryugin Ilya

  KEYWORDS: Integral Equations, Solvability, Solution Construction, Controllability, Minimizing Sequences

  JOURNAL NAME: Journal of Applied Mathematics and Physics, Vol.12 No.2, February 29, 2024

  ABSTRACT: The issues of solvability and construction of a solution of the Fredholm integral equation of the first kind are considered. It is done by immersing the original problem into solving an extremal problem in Hilbert space. Necessary and sufficient conditions for the existence of a solution are obtained. A method of constructing a solution of the Fredholm integral equation of the first kind is developed. A constructive theory of solvability and construction of a solution to a boundary value problem of a linear integrodifferential equation with a distributed delay in control, generated by the Fredholm integral equation of the first kind, has been created.