# Periodic solutions for implicit evolution inclusions

## TL;DR

This paper proves the existence of periodic solutions for a class of nonlinear implicit evolution inclusions in Hilbert spaces, using approximation methods and surjectivity results for parabolic operators.

## Contribution

It introduces a novel approach combining approximation techniques and surjectivity results to establish periodic solutions for nonlinear implicit evolution inclusions.

## Key findings

- Existence of periodic solutions established.
- Applicable to nonlinear, nonmonotone, time-varying set-valued maps.
- Method extends to evolution equations in Hilbert spaces.

## Abstract

We consider a nonlinear implicit evolution inclusion driven by a nonlinear, nonmonotone, time-varying set-valued map and defined in the framework of an evolution triple of Hilbert spaces. Using an approximation technique and a surjectivity result for parabolic operators of monotone type, we show the existence of a periodic solution.