Displaying similar documents to “Topological structure of solution sets of differential inclusions: the constrained case.”

On the semilinear multi-valued flow under constraints and the periodic problem

Ralf Bader (2000)

Commentationes Mathematicae Universitatis Carolinae

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* * In the paper we will be concerned with the topological structure of the set of solutions of the initial value problem of a semilinear multi-valued system on a closed and convex set. Assuming that the linear part of the system generates a C 0 -semigroup we show the R δ -structure of this set under certain natural boundary conditions. Using this result we obtain several criteria for the existence of periodic solutions for the semilinear system. As an application the problem...

Lower semicontinuous differential inclusions. One-sided Lipschitz approach

Tzanko Donchev (1998)

Colloquium Mathematicae

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Some properties of differential inclusions with lower semicontinuous right-hand side are considered. Our essential assumption is the one-sided Lipschitz condition introduced in [4]. Using the main idea of [10], we extend the well known relaxation theorem, stating that the solution set of the original problem is dense in the solution set of the relaxed one, under assumptions essentially weaker than those in the literature. Applications in optimal control are given.

Near viability for fully nonlinear differential inclusions

Irina Căpraru, Alina Lazu (2014)

Open Mathematics

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We consider the nonlinear differential inclusion x′(t) ∈ Ax(t) + F(x(t)), where A is an m-dissipative operator on a separable Banach space X and F is a multi-function. We establish a viability result under Lipschitz hypothesis on F, that consists in proving the existence of solutions of the differential inclusion above, starting from a given set, which remain arbitrarily close to that set, if a tangency condition holds. To this end, we establish a kind of set-valued Gronwall’s lemma...