# Disjoint Li-Yorke chaos in Fr\'echet spaces

## TL;DR

This paper explores various forms of disjoint Li-Yorke chaos in sequences of multivalued linear operators within Fréchet spaces, extending to continuous cases and applying findings to abstract partial differential equations.

## Contribution

It introduces new notions of disjoint Li-Yorke chaos in Fréchet spaces and their continuous analogues, with applications to partial differential equations.

## Key findings

- Different notions of disjoint Li-Yorke chaos are formulated and analyzed.
- Applications to abstract partial differential equations demonstrate practical relevance.

## Abstract

The main aim of this paper is to consider various notions of (dense) disjoint Li-Yorke chaos for general sequences of multivalued linear operators in Fr\' echet spaces. We also consider continuous analogues of introduced notions and provide certain applications to the abstract partial differential equations.