ω-Limit Sets for Differential Inclusions

  • Asen L. DontchevEmail author
  • Mikhail I. Krastanov
  • Vladimir M. Veliov
Part of the Springer INdAM Series book series (SINDAMS, volume 11)


This paper is about locating ω-limit sets for solutions of differential inclusions with not necessarily continuous right side. Based on the LaSalle principle we assume that as time \(t \rightarrow \infty\) the set of solutions approaches a closed subset \(\mathcal{S}\) of \(\mathbb{R}^{n}\) and then consider the dynamics restricted on \(\mathcal{S}\) to find the location of the ω-limit set by utilizing nonsmooth Lyapunov type functions over a neighborhood of \(\mathcal{S}\); then we prove that this location is also valid for the original dynamics. We apply our result for nonsmooth differential equations and compare it with some recent works.


Lyapunov Function Differential Inclusion Lipschitz Continuous Function Lyapunov Function Versus Original Dynamic 
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A.L. Dontchev gratefully acknowledges the support from the National Science Foundation Grant DMS 1008341 through the University of Michigan.

M.I. Krastanov gratefully acknowledges the support from the Sofia University “St. Kliment Ohridski” under contract No. 08/26.03.2015.

V.M. Veliov gratefully acknowledges the support from Austrian Science Foundation (FWF) Grant P 26640-N25.


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Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  • Asen L. Dontchev
    • 1
    Email author
  • Mikhail I. Krastanov
    • 2
    • 3
  • Vladimir M. Veliov
    • 4
  1. 1.Mathematical ReviewsAnn ArborUSA
  2. 2.Faculty of Mathematics and InformaticsUniversity of SofiaSofiaBulgaria
  3. 3.Bulgarian Academy of SciencesInstitute of Mathematics and InformaticsSofiaBulgaria
  4. 4.Institute of Mathematical Methods in EconomicsVienna University of TechnologyViennaAustria

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