# A Nonlinear Evolution Equation in an Ordered Banach Space, Reconsidered

## TL;DR

This paper extends previous results on nonlinear evolution equations from Lebesgue spaces to more general ordered Banach spaces, correcting a technical error and broadening the theoretical framework.

## Contribution

It generalizes existence results for nonlinear evolution equations to ordered Banach spaces without requiring a Banach lattice structure.

## Key findings

- Existence of solutions is established in a broader setting.
- A technical error in prior work is identified and corrected.
- The results apply to kinetic theory models in more general spaces.

## Abstract

Results of a previous paper [Commun. Contemp. Math., 09 (2007) 217-251] on the existence of solutions to a nonlinear evolution equation in an abstract Lebesgue space, arising from kinetic theory, are re-obtained in the more general setting of a real ordered Banach space, with additive norm on the positive cone, which is not necessarily a (Banach) lattice. In addition, an easily correctable technical error in the aforementioned paper is pointed out, and repaired.