Asymptotic Behavior of a Class of Evolution Variational Inequalities

Abstract

We establish a new LaSalle's invariance principle and discuss the asymptotic behavior of a class of first-order evolution variational inequalities.

Locating Theorems of Differential Inclusions Governed by Maximally Monotone Operators

“…It also generalizes the results in [23], since it can be applicable to the case where the function f is replaced by a CUSCO multifunction. In addition, the proposed invariance principle clearly covers the one given in [36], where the operator A is the Fenchel subdifferential of an extended-real-valued, convex, proper and lower semicontinuous function.…”

“…• Theorem 4.5 and Theorem 4.6 can be considered, respectively, as generalization and refinement of the LaSalle's invariance theorem given in [36]. More precisely, Theorem 4.6 provides a better location of the ω-limit set in terms of the invariant sets.…”

“…More precisely, Theorem 4.6 provides a better location of the ω-limit set in terms of the invariant sets. In [36], the author shows that the ω-limit set is also contained in the largest invariant set M, of the set E := {x ∈ S : f (x), ∇V (x) + ϕ(x) − ϕ(x − ∇V (x)) = 0}, which is contained in M S . While, Theorem 4.6 gives the following location of the ω-limit set ω(x 0 ) ⊂ M α ⊂ M ⊂ M S ⊂ S.…”