Solution Sets Of Differential Inclusions Research Articles

On local solutions of degenerate differential inclusions

We study the existence and properties of local solution sets for differential inclusions of the form (Ax)′ ∈ F(t, x), where A is a closed linear surjective operator with nontrivial null space and F is a compact set-valued mapping.

On the solution sets of differential inclusions and the periodic problem in Banach spaces

In this paper, the topological structure of the solution set of a constrained semilinear differential inclusion in a Banach space E is studied. It is shown that the set of all mild solutions, with values in a closed and, in general, thin subset D⊂ E, is an R δ -set provided natural boundary conditions and appropriate geometrical assumptions on D (which hold, e.g. when D is convex) are satisfied. Applications to the periodic problem and to the existence of equilibria are given.

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 generalize the known theorems about the structure of viable solution set for differential inclusions.

Topological structure of solution sets of differential inclusions: the constrained case

We survey and announce some current results on the existence, the viability, and the topological structure of the viable solutions of differential equations and inclusion in Banach spaces under set constraints. Some new results concerning semilinear differential inclusions with state variables constrained to the so‐called regular and strictly regular sets, together with their applications, are presented and discussed.

On the Topological Regularity of the Solution Set of Differential Inclusions with Constraints

In this paper we establish the topological regularity of the solution set of differential inclusions with constraints, defined in R n . The result is then extended to systems defined in Banach spaces. Our proof makes. use of an approximation result by Lipschitz functions of Caratheodory functions, which we also prove in this paper.

On the Continuous Dependence on Parameter of the Solution Set of Differential Inclusions

On the Continuous Dependence on Parameter of the Solution Set of Differential Inclusions

On the solution set of differential inclusions in Banach space

On the solution set of differential inclusions in Banach space

On the Solution Set of Differential Inclusions with State Constraints

In this paper we consider differential inclusions in R m with time varying state constraints, of the form: −x(t) eN (x(t)) K(t) + F(t,x(t)), x(0) ≡ x(0) Here N(x) denotes the normal cone to k(t)at x. We prove that the solution set of this inclusion is an Rδ-set in C(T,R m). For the special case when k(t)-K (independent of t), our result also characterizes the solution set of the projected differentional inclusion and also help us establish the existence of periodic trajectories

A property of the solution set of differential inclusions in banach spaces with a caratheodory orientor field

We examine the solution set of differential inclusions in separable Banach spaces with a Caratheodory orientor field i.e. teF(t ,x) is measurable and xeF(t,x) is completely u.s.c. We show that the solution set is an Rδ set in C(T,X), extending this way earlier results by Lasry-Robert, Himmelberg-Van Vleck, De Blasi - Myjak and Papageorgiou

On the solution set of differential inclusions in banach space

Let X be a separable Banach space and F(•,•) an orientor field from [0,b]xX into the nonempty, compact, convex subsets of X, which is completely Hausdorff upper semicontinuous and We show that solution set of the multivalued Cauchy problem set in Cχ

On the solution sets of differential inclusions

On the solution sets of differential inclusions

A note on the solution sets of differential inclusions

A note on the solution sets of differential inclusions