On the properties of solutions to the Goursat--Darboux problem with boundary and distributed controls.
On the properties of the solution set of nonconvex evolution inclusions of the subdifferential type
In this paper we consider nonconvex evolution inclusions driven by time dependent convex subdifferentials. First we establish the existence of a continuous selection for the solution multifunction and then we use that selection to show that the solution set is path connected. Two examples are also presented.
On the second-order contingent set and differential inclusions.
On the set of solutions of some nonconvex nonclosed hyperbolic differential inclusions
We consider a class of nonconvex and nonclosed hyperbolic differential inclusions and we prove the arcwise connectedness of the solution set.
On the set-valued calculus in problems of viability and control for dynamic processes : the evolution equation
On the Solution Set of a Nonconvex Nonclosed Second Order Inclusion
We consider a nonconvex and nonclosed second-order evolution inclusion and we prove the arcwise connectedness of the set of its mild solutions.
On the solution set of a two point boundary value problem.
On the solution set of nonconvex subdifferential evolution inclusions
On the solution set of the nonconvex sweeping process
We prove that the solutions of a sweeping process make up an -set under the following assumptions: the moving set C(t) has a lipschitzian retraction and, in the neighbourhood of each point x of its boundary, it can be seen as the epigraph of a lipschitzian function, in such a way that the diameter of the neighbourhood and the related Lipschitz constant do not depend on x and t. An application to the existence of periodic solutions is given.
On the structure of the solution set of evolution inclusions with time-dependent subdifferentials
On the tangency of multifunctions
On the theorem of Filippov-Pliś and some applications
On the theory of functional-differential inclusions of neutral type.
On the theory of one-sided models in spaces with arbitrary cones.
On the topological structure of the solution set for a semilinear ffunctional-differential inclusion in a Banach space
In this paper we show that the set of all mild solutions of the Cauchy problem for a functional-differential inclusion in a separable Banach space E of the form x’(t) ∈ A(t)x(t) + F(t,xt) is an -set. Here A(t) is a family of linear operators and F is a Carathéodory type multifunction. We use the existence result proved by V. V. Obukhovskiĭ [22] and extend theorems on the structure of solutions sets obtained by N. S. Papageorgiou [23] and Ya. I. Umanskiĭ [32].
On the two-point boundary value problem for quadratic second-order differential equations and inclusions on manifolds.
Optimal solutions to stochastic differential inclusions
A martingale problem approach is used first to analyze compactness and continuous dependence of the solution set to stochastic differential inclusions of Ito type with convex integrands on the initial distributions. Next the problem of existence of optimal weak solutions to such inclusions and their dependence on the initial distributions is investigated.
Optimization of discrete and differential inclusions of Goursat-Darboux type with state constraints.
Oscillatory and nonoscillatory solutions for first order impulsive dynamic inclusions on time scales
In this paper we discuss the existence of oscillatory and nonoscillatory solutions for first order impulsive dynamic inclusions on time scales. We shall rely of the nonlinear alternative of Leray-Schauder type combined with lower and upper solutions method.
Oscillatory and nonoscillatory solutions for first order impulsive differential inclusions
In this paper we discuss the existence of oscillatory and nonoscillatory solutions of first order impulsive differential inclusions. We shall rely on a fixed point theorem of Bohnenblust-Karlin combined with lower and upper solutions method.