Abstract
ABSTRACT Our main result is the following: let be a multifunction, and assume that there exists a neglegible subset , satisfying a certain geometrical condition, such that the restriction of F to is bounded, lower semicontinuous with non-empty closed values, and its range belongs to a certain family defined below. Then, there exists a bounded multifunction such that G is upper semicontinuous with non-empty compact convex values, and every generalized solution of is a solution of . Such a result improves a celebrated result by A. Bressan, valid for lower semicontinuous multifunctions. We point out that a multifunction F satisfying our assumptions can fail to be lower semicontinuous even at all points . We derive some existence and qualitative results for the Cauchy problem associated to such a class of multifunctions. As an application, we prove existence and qualitative results for the implicit Cauchy problem , , with f discontinuous in u.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
