Approximate invariance and differential inclusions in Hilbert spaces

  title={Approximate invariance and differential inclusions in Hilbert spaces},
  author={F. H.A. and Sergei Yu. and M. Li},
Consider a mapping F from a Hilbert space H to the subsets of H which is upper semicontinuous/Lipschitz, has nonconvex, noncompact values and satisfies to a linear growth condition. We give necessary and sufficient conditions for a subset S of H to be approximately weak/strong invariant with respect to approximate solutions of the differential inclusion ẋ(t) ∈ F (x). The conditions are given in terms of the lower/upper Hamiltonians corresponding to F and involve nonsmooth analysis elements and… CONTINUE READING

From This Paper

Figures, tables, results, connections, and topics extracted from this paper.
10 Extracted Citations
16 Extracted References
Similar Papers

Referenced Papers

Publications referenced by this paper.
Showing 1-10 of 16 references

Generalized gradients and applications

  • F. H. Clarke
  • Trans. Amer. Math. Soc. 205
  • 1975
Highly Influential
7 Excerpts

Differential inclusions in Banach spaces

  • A. A. Tolstonogov
  • Nauka, Novosibirsk
  • 1986
Highly Influential
4 Excerpts

Optimal control via nonsmooth analysis

  • P. D. Loewen
  • (Providence), CRM Proceedings and Lecture Notes…
  • 1993
1 Excerpt

Viability theory

  • J.-P. Aubin
  • Birkhauser, Boston
  • 1991
3 Excerpts

Strongly and weakly invariant sets with respect to differential inclusions

  • Kh. Guseinov, V. N. Ushakov
  • Differencial nye Urakneniya
  • 1990
2 Excerpts

Positional differential games

  • N. N. Krasovskii, A. I. Subbotin
  • Nauka, Moscow, 1974,
  • 1988
2 Excerpts

Differential inclusions

  • J.-P. Aubin, A. Cellina
  • Springer-Verlag, New York
  • 1984
3 Excerpts

A generalizations of the basic equation of the theory of differential games

  • A. I. Subbotin
  • Soviet Math. Dokl. 22
  • 1980
1 Excerpt

Introduction to nonsmooth analysis , textbook in preparation . [ 10 ] , Qualitative properties of trajectories of control systems : a survey

  • Yu. S. Ledyaev, R. J. Stern, P. R. Wolenski
  • J . Dynamical and Control Systems
  • 1977

Similar Papers

Loading similar papers…