Invariant Measures of Differential Inclusions Applied to Singular Perturbations

Monotone Invariant Solutions to Differential Inclusions

Let a given set be endowed with a preference preordering, and consider the problem of finding a solution to the differential inclusion A(OeS(*(O) which remains in the given set and evolves monotonically with respect to the preordering. We give sufficient conditions for the existence of such a trajectory, couched in terms of a notion of tangency developed by Clarke. No smoothness or convexity is...

Singular perturbations of integro-differential equations

We study the singular perturbation problem (E2) 2 2u′′ 2 (t) + u ′ 2(t) = Au2(t) + (K ∗Au2)(t) + f2(t), t ≥ 0, 2 > 0, for the integrodifferential equation (E) w′(t) = Aw(t) + (K ∗Aw)(t) + f(t), t ≥ 0, in a Banach space, when 2 → 0. Under the assumption that A is the generator of a strongly continuous cosine family and under some regularity conditions on the scalar-valued kernel K we show that p...

Regular and Singular Perturbations of Upper Semicontinuous Differential Inclusion

In the paper we study the continuity properties of the solution set of upper semicontinuous differential inclusions in both regularly and singularly perturbed case. Using a kind of dissipative type of conditions introduced in [1] we obtain lower semicontinuous dependence of the solution sets. Moreover new existence result for lower semicontinuous differential inclusions is proved.

Stability, Bifurcations and Stabilisation of Invariant Sets in Differential Inclusions

THE FULL AVERAGING OF FUZZY DIFFERENTIAL INCLUSIONS

In this paper the substantiation of the method of full averaging for fuzzy differential inclusions is considered. These results generalize the results of [17, 20] for differential inclusions with Hukuhara derivative and of [18] for fuzzy differential equations.