Abstract
We focus on a very general problem in the theory of dynamic systems, namely that of studying measure differential inclusions with varying measures. The multifunction on the right hand side has compact non-necessarily convex values in a real Euclidean space and satisfies bounded variation hypotheses with respect to the Pompeiu excess (and not to the Hausdorff-Pompeiu distance, as usually in literature). This is possible due to the use of interesting selection principles for excess bounded variation set-valued mappings. Conditions for the minimization of a generic functional with respect to a family of measures generated by equiregulated left-continuous, nondecreasing functions and to associated solutions of the differential inclusion driven by these measures are deduced, under constraints only on the initial point of the trajectory.
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Acknowledgements
The authors are greatly indebted to the associate editor and to the two referees for their insightful comments and constructive suggestions.
This research has been partially supported by GNAMPA, prot. U-UFMBAZ-2018-000351. The third author has been supported by GNAMPA, prot. U-UFMBAZ-2018-001501 and by “Excellence in Advanced Research, Leadership innovation and Patenting for University and Regional Development” - EXCALIBUR, Grant Contract no. 18PFE / 10.16.2018 Institutional Development Project - Funding for Excellence in RDI, Program 1 - Development of the National R & D System, Subprogram 1.2 - Institutional Performance, National Plan for Research and Development and Innovation for the period 2015-2020 (PNCDI III).
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Di Piazza, L., Marraffa, V. & Satco, B. Measure Differential Inclusions: Existence Results and Minimum Problems. Set-Valued Var. Anal 29, 361–382 (2021). https://doi.org/10.1007/s11228-020-00559-9
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DOI: https://doi.org/10.1007/s11228-020-00559-9