Nonlinear evolution equations with a non-Lipschitz perturbation: convergence of successive approximations and uniqueness of solutions

TL;DR

This paper studies the existence and uniqueness of solutions for nonlinear evolution equations with non-Lipschitz perturbations in Banach spaces, focusing on convergence of approximations.

Contribution

It establishes conditions for solution existence and uniqueness despite the perturbation lacking Lipschitz continuity.

Findings

Proves convergence of successive approximations.

Demonstrates uniqueness of solutions under non-Lipschitz perturbations.

Provides theoretical framework for nonlinear evolution equations with non-Lipschitz terms.

Abstract

This paper investigates the existence and uniqueness of solutions for a nonlinear evolution equation governed by an m-accretive operator A in a Banach space, presenting a perturbation term that does not satisfy the Lipschitz condition.