Regularization and Parameter Choice for the Third Kind Nonlinear Volterra-Stieltjes Integral Equation Solutions

Abstract

The article considers nonlinear Volterra-Stieltjes integral equations of the third kind, and its solution by regularizing operator according to M. M. Lavrentev. A uniqueness theorem was proved, and a regularization parameter was chosen. The research uses the concept of a derivative with respect to an increasing function, the method of regularization according to M. M. Lavrentevs methods in functional analysis, methods of transformation of equations, methods of integral and differential equations. Proposed methods can be used to study the integral, integral-differential equations of the Volterra-Stieltjes type of high orders, as well as in the qualitative study of some applied processes in the field of physics, ecology, medicine, and the theory of control complex systems. They can be used in the further development of the theory of integral equations in classes of incorrect problems, in numerical solution of Volterra-Stieltjes integral equations of the third kind, and when solving specific applied problems that lead to equations of the third kind.