Nonlinear the first kind Fredholm integro-differential first-order equation with degenerate kernel and nonlinear maxima

In this note, the problems of solvability and construction of solutions for a nonlinear Fredholm one-order integro-differential equation with degenerate kernel and nonlinear maxima are considered. Using the method of degenerate kernel combined with the method of regularization, we obtain an implici...

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Bibliographic Details
Main Authors: Yuldashev, T. K., Eshkuvatov, Z. K., Nik Long, N. M. A.
Format: Article
Published: Lviv Polytechnic National University 2022
Online Access:http://psasir.upm.edu.my/id/eprint/102325/
Description
Summary:In this note, the problems of solvability and construction of solutions for a nonlinear Fredholm one-order integro-differential equation with degenerate kernel and nonlinear maxima are considered. Using the method of degenerate kernel combined with the method of regularization, we obtain an implicit the first-order functional-differential equation with the nonlinear maxima. Initial boundary conditions are used to ensure the solution uniqueness. In order to use the method of a successive approximations and prove the one value solvability, the obtained implicit functional-differential equation is transformed to the nonlinear Volterra type integro-differential equation with the nonlinear maxima.