Existence and Destruction of Kantorovich Main Continuous Solutions of Nonlinear Integral Equations

TL;DR

This paper establishes conditions for the existence of main solutions to nonlinear Volterra integral equations, introduces a method to compute boundary intervals, and demonstrates the technique's effectiveness through examples.

Contribution

It provides new sufficient conditions for solution existence and a computational method for boundary intervals in nonlinear integral equations.

Findings

Conditions for existence of solutions are derived.

A method for computing boundary intervals is proposed.

The technique is validated with concrete examples.

Abstract

The sufficient conditions are obtained for existence of the main solution of the nonlinear Volterra integral equation of the second kind on the semi-axis and on a finite interval. The method for computation of this boundary interval is designed. Beyond such integral the solution has the blow-up. The efficiency of proposed technique is demonstrated on concrete examples.