# Asymptotic behavior of time periodic solutions for extended Fisher-Kolmogorov equations with delays

## TL;DR

This paper studies the existence, uniqueness, and stability of time-periodic solutions for extended Fisher-Kolmogorov equations with delays, providing a general framework using operator semigroup theory.

## Contribution

It introduces a new framework for finding time-periodic solutions to delayed nonlinear Fisher-Kolmogorov equations, expanding analytical tools in this area.

## Key findings

- Established conditions for existence and stability of solutions.
- Developed a general method applicable to nonlinear delayed equations.
- Provided theoretical insights into the asymptotic behavior of solutions.

## Abstract

In this paper, we investigate the global existence, uniqueness and asymptotic stability of time $\omega$-periodic classical solution for a class of extended Fisher-Kolmogorov equations with delays and general nonlinear term. We establish a general framework to find time $\omega$-periodic solutions for nonlinear extended Fisher-Kolmogorov equations with delays and general nonlinear function, which will provide an effective way to deal with such kinds of problems. The discussion is based on the theory of compact and analytic operator semigroups and maximal regularization method.