Abstract
Inf-compactness of the objective functional in an abstract variational problem, where the dynamical system consists of a linear functional-integral equation, is proven by suitably topologizing the space of relaxed control functions. The topology is obtained quite naturally from a Hilbert cube compactification of the space of control points. Under additional convexity assumptions a general existence result, implying that of A. D. Ioffe ( Dokl. Akad. Nauk SSSR 205 (1972), 277–280; Soviet Math. Dokl. 13 (1972), 919–923) is proven.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Disclaimer: 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.