Disjoint Li-Yorke chaos in Fréchet spaces

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 Fréchet spaces. We also consider continuous analogues of introduced notions and provide certain applications to the abstract partial differential equations.2010 Mathematics Subject Classification. 47A06, 47A16.

Reiterative $m_{n}$-distributional chaos of type $s$ in Fr\' echet spaces

“…(i) It is worth noting that Theorem 4.1 and Theorem 4.13 provide extensions of [10, Theorem 3.1, Corollary 3.2], where the orbits of an operator in Banach space have been considered. (ii) A slight generalization of Theorem 4.13 for disjoint Li-Yorke chaotic operators has been recently established and proved in [28]. Now we will state and prove the following result, which is closely linked with Theorem 4.1 and Theorem 4.13: Theorem 4.15.…”