  In this paper, we are interested in studying the asymptotic behavior of the
solutions of differential inclusions governed by maximally monotone operators.
In the case where the LaSalle's invariance principle is inconclusive, we
provide a refined version of the invariance principle theorem. This result
derives from the problem of locating the $\omega$-limit set of a bounded
solution of the dynamic. In addition, we propose an extension of LaSalle's
invariance principle, which allows us to give a sharper location of the
$\omega$-limit set. The provided results are given in terms of nonsmooth
Lyapunov pair-type functions.
