S.B. Zаriроv

Annotation:

This research examines a model integral equation in the one-dimensional case. The equation under consideration possesses two boundary points, and its study was conducted within the framework of the theory of integro-differential equations. To prove the existence and convergence of integral representations, the application of asymptotic conditions was deemed necessary. It should be noted that the general solution of this model equation contains an arbitrary function. In cases where the general solution consists of arbitrary constants, a boundary value problem was formulated and investigated. Furthermore, the conditions under which the given equation possesses a unique solution were studied. It is worth noting that if the integral equation has a unique solution, it is not required to set the boundary conditions, because the solution does not contain arbitrary constants. In those cases when the solution includes arbitrary constants, the boundary conditions are applied accordingly. Finally, based on the obtained scientific results, relevant theorems and conclusions are presented.

Kеуwоrds: one-dimensional model integral, internal and boundary points, boundary problems, asymptotic conditions, given constants.