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

作　　者：Aisagaliev Serikbai Nurmagambetov Dias Sevryugin Ilya Aisagaliev Serikbai;Nurmagambetov Dias;Sevryugin Ilya(Differential Equations and Control Theory, Al-Farabi Kazakh National University, Almaty, Kazakhstan;Department of Mathematics, Prairie View A&M University, Prairie View, USA)

机构地区：[1]Differential Equations and Control Theory, Al-Farabi Kazakh National University, Almaty, Kazakhstan [2]Department of Mathematics, Prairie View A&M University, Prairie View, USA

出　　处：《Journal of Applied Mathematics and Physics》2024年第2期720-735,共16页应用数学与应用物理（英文）

摘　　要：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.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.

关 键 词：Integral Equations SOLVABILITY Solution Construction CONTROLLABILITY Minimizing Sequences 

分 类 号：O17[理学—数学]