Tzanko Donchev

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where H is a Hilbert space, and where F : T ×H → H is a set-valued mapping with nonempty compact values (some results hold also with no compactness assumption). It is well known that the differential inclusion description under consideration is important for its own sake and covers many other conventional and nonconventional models involving dynamical(More)
We study discrete approximations of nonconvex differential inclusions in Hilbert spaces and dynamic optimization/optimal control problems involving such differential inclusions and their discrete approximations. The underlying feature of the problems under consideration is a modified one-sided Lipschitz condition imposed on the right-hand side (i.e., on the(More)
The notions of relaxed submonotone and relaxed monotone mappings in Banach spaces are introduced and many of their properties are investigated. For example, the Clarke subdifferential of a locally Lipschitz function in a separable Banach space is relaxed submonotone on a residual subset. For example, it is shown that this property need not be valid on the(More)
In the paper, we study weak invariance of differential inclusions with non-fixed time impulses under compactness type assumptions. When the right-hand side is one sided Lipschitz an extension of the well known relaxation theorem is proved. In this case also necessary and sufficient condition for strong invariance of upper semi continuous systems are(More)
A two point boundary value problem for differential inclusions with relaxed one sided Lipschitz right-hand side in Banach spaces with uniformly convex duals are studied. We use successive approximations to obtain nonemptiness and compactness of the solution set as well as its continuous dependence from the initial conditions and the right-hand side. The(More)
This paper is a natural exstension of [7J. We examine the main qualitative properties of the solution set of differential inclusion with the lag. The right-hand side is supposed to be one side Lipschitz and with almost continuous convex hull. Afterwards we prove the existence of solutions when the right-hand side is a sum of one side Lipschitz and almost(More)