Sharkovskii's theorem, differential inclusions, and beyond

An Infinite-time Relaxation Theorem for Differential Inclusions

The fundamental relaxation result for Lipschitz differential inclusions is the Filippov-Wažewski Relaxation Theorem, which provides approximations of trajectories of a relaxed inclusion on finite intervals. A complementary result is presented, which provides approximations on infinite intervals, but does not guarantee that the approximation and the reference trajectory satisfy the same initial ...

Filippov’s Theorem for Impulsive Differential Inclusions with Fractional Order

In this paper, we present an impulsive version of Filippov’s Theorem for fractional differential inclusions of the form: D ∗ y(t) ∈ F (t, y(t)), a.e. t ∈ J\{t1, . . . , tm}, α ∈ (1, 2], y(t+k )− y(t − k ) = Ik(y(t − k )), k = 1, . . . ,m, y(t+k )− y (t−k ) = Ik(y (t−k )), k = 1, . . . ,m, y(0) = a, y′(0) = c, where J = [0, b], D ∗ denotes the Caputo fractional derivative and F is a setvalued ma...

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.

Improving the Solution of Fuzzy Differential Inclusions

Covering dimension and differential inclusions

In this paper we shall establish a result concerning the covering dimension of a set of the type {x ∈ X : Φ(x)∩Ψ(x) 6= ∅}, where Φ, Ψ are two multifunctions from X into Y and X, Y are real Banach spaces. Moreover, some applications to the differential inclusions will be given.