Representation of the Attainable Set for Lipschitzian Differential Inclusions

Continuous Selections of Solution Sets of Lipschitzian Quantum Stochastic Differential Inclusions

“…Some selection results at the classical setting can be found in the works of Cellina (1988), Aubin and Cellina (1984), Fryszkowski (1983), Antosiewicz and Cellina (1975), Colombo et al (1991) and the book by Repovs and Semenov (1998). As shown in the work of Cellina and Ornelas (1992) selection results have been used to show that the solution set -map and the attainable set admit some continuous parameterizations.…”

On Semicontinuous Nonclassical Ordinary Differential Inclusions with Nonlocal Condition

“…The following were considered: the case when the set-valued map is a non-open multifunction with measurability and Lipschitz continuity conditions imposed on the first and second variables respectively. These recent studies have shown that differential inclusions and problems with nonlocal conditions are of more practical applications in real life when compared to problems with local conditions (Antosiewicz and Cellina, 1975;Bishop et al, 2016;Cellina, 1988).…”

Continuous selections of solution sets to evolution equations

“…where F is Lipschitzian with respect to x , was proved first by Cellina in [5], under the assumption that the values of F are nonempty compact sets contained in a bounded subset of 7?". The case in which F takes nonempty closed values in 7?"…”

“…The case in which F takes nonempty closed values in 7?" was considered in [6]. Some extensions to Lipschitzian F , with nonempty closed values, in a separable Banach space X were treated in [3,7].…”