Measure differential inclusions: existence results and minimum problems

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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 possi- ble 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 solu- tions of the differential inclusion driven by these measures are deduced, under constraints only on the initial point of the trajectory.
Original languageEnglish
Number of pages21
JournalSet-Valued and Variational Analysis
Publication statusPublished - 2020

All Science Journal Classification (ASJC) codes

  • Analysis
  • Statistics and Probability
  • Numerical Analysis
  • Geometry and Topology
  • Applied Mathematics

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