On some strengthening of the global implicit function theorem with an application to a Cauchy problem for an integro-differential Volterra system

TL;DR

This paper enhances the global implicit function theorem, providing stronger conditions for existence, uniqueness, and differentiability, and applies these results to a Cauchy problem involving a nonconvolution integro-differential Volterra system.

Contribution

It offers improved theoretical conditions for the global implicit function theorem and applies these to a specific Cauchy problem for a Volterra system.

Findings

Established stronger existence and uniqueness results.

Proved differentiability of the implicit function under new conditions.

Applied the theoretical results to a nonconvolution Volterra system.

Abstract

In the paper, we improve our earlier results concerning the existence, uniqueness and differentiability of a global implicit function. Some application to a Cauchy problem for an integro-differential Volterra system of nonconvolution type, is given.