Abstract
In the setting of 2-uniformly smooth and q -uniformly convex Banach spaces, we prove the existence of solutions of the following multivalued differential equation: -\frac{d}{dt} J(u(t)) \in N^C(C(t,u(t));u(t)) \text{ a.e. in } [0,T]. \:\:\: \mathrm{(SDNSP)} This inclusion is called State Dependent Nonconvex Sweeping Process (SDNSP). Here N^C(C(t,u(t)); u(t)) stands for the Clarke normal cone. The perturbed (SDNSPP) is also considered. Our results extend recent existing results from the setting of Hilbert spaces to the setting of Banach spaces. In our proofs we use some new results on V -uniformly generalized prox-regular sets in Banach spaces.
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.
