Nonconvolution nonlinear integral Volterra equations with monotone operators

TL;DR

This paper investigates the existence, uniqueness, and behavior of solutions for nonlinear Volterra integral equations with non-convolution kernels, extending known results from convolution cases using comparison techniques.

Contribution

It introduces a broad class of nonconvolution Volterra equations whose solutions mirror those of convolution-based equations, enhancing understanding of their solution properties.

Findings

Established conditions for existence and uniqueness of solutions.

Identified classes where solutions exhibit attractive behavior.

Extended comparison techniques to non-convolution kernels.

Abstract

Some results about existence, uniqueness, and attractive behaviour of solutions for nonlinear Volterra integral equations with non-convolution kernels are presented in this paper. These results are based on similar ones about nonlinear Volterra integral equations with convolution kernels and some comparison techniques. Therefore, this paper is devoted to find a wide class of nonconvolution Volterra integral equations where their solutions behave like those of Volterra equations with convolution kernels.