Topological Structure of Solution Sets of Differential Inclusions: the Constrained Case

Differential Inclusions with Constraints in Banach Spaces

The paper provides topological characterization for solution sets of differential inclusions with (not necessarily smooth) functional constraints in Banach spaces. The corresponding compactness and tangency conditions for the right hand-side are expressed in terms of the measure of noncompactness and the Clarke generalized gradient, respectively. The consequences of the obtained result generali...

On the averaging of differential inclusions with Fuzzy right hand side with the average of the right hand side is absent

In this article we consider the averaging method for differential inclusions with fuzzy right-hand side for the case when the limit of a method of an average does not exist. 

Improving the Solution of Fuzzy Differential Inclusions

Impulsive neutral functional differential inclusions in Banach spaces

In this paper, we first present an impulsive version of Filippov’s Theorem for first-order neutral functional differential inclusions of the form, d dt [y(t)− g(t, yt)] ∈ F (t, yt), a.e. t ∈ J\{t1, . . . , tm}, y(t+k )− y(tk ) = Ik(y(tk )), k = 1, . . . , m, y(t) = φ(t), t ∈ [−r, 0], where J = [0, b], F is a set-valued map and g is a single-valued function. The functions Ik characterize the jum...

Structure of Solutions Sets and a Continuous Version of Filippov’s Theorem for First Order Impulsive Differential Inclusions with Periodic Conditions

In this paper, the authors consider the first-order nonresonance impulsive differential inclusion with periodic conditions y′(t)− λy(t) ∈ F (t, y(t)), a.e. t ∈ J\{t1, . . . , tm}, y(t+k )− y(t − k ) = Ik(y(t − k )), k = 1, 2, . . . ,m, y(0) = y(b), where J = [0, b] and F : J × R → P(R) is a set-valued map. The functions Ik characterize the jump of the solutions at impulse points tk (k = 1, 2, ....