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

Locating Theorems of Differential Inclusions Governed by Maximally Monotone Operators