ω-Limit Sets for Differential Inclusions

Abstract

This paper is about locating ω-limit sets for solutions of differential inclusions with not necessarily continuous right side. Based on the LaSalle principle we assume that as time $t \rightarrow \infty$ the set of solutions approaches a closed subset $\mathcal{S}$ of $\mathbb{R}^{n}$ and then consider the dynamics restricted on $\mathcal{S}$ to find the location of the ω-limit set by utilizing nonsmooth Lyapunov type functions over a neighborhood of $\mathcal{S}$; then we prove that this location is also valid for the original dynamics. We apply our result for nonsmooth differential equations and compare it with some recent works.