Hostname: page-component-7bb8b95d7b-qxsvm Total loading time: 0 Render date: 2024-09-26T14:14:17.170Z Has data issue: false hasContentIssue false
  • English
  • Français

On an existence result for nonlinear evolution inclusions

Published online by Cambridge University Press:  20 January 2009

Stanislaw Migórski
Stanislaw Migórski
Affiliation:
Institute For Information SciencesJagellonian UniversityUL. Nawojki 1130072 Cracow, Poland
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

In this paper we present an existence result for a class of nonlinear evolutions inclusions. A result on the compactness of the solution set for a differential inclusion is also established.

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 39 , Issue 1 , February 1996 , pp. 133 - 141
Copyright
Copyright © Edinburgh Mathematical Society 1996

References

REFERENCES

1. Ahmed, N. U. and Teo, K. L., Optimal Control of Distributed Parameter Systems (North-Holland, New York, New York, 1981).Google Scholar
2. Aubin, J. P. and Cellina, A., Differential Inclusions (Springer-Verlag, Berlin-Heidelberg-New York-Tokyo, 1984).CrossRefGoogle Scholar
3. Barbu, V., Nonlinear Semigroups and Differential Equations in Banach Spaces (Noordhoff International Publishing, Leyden, The Netherlands, 1976).CrossRefGoogle Scholar
4. Lions, J. L., Quelques méthodes de résolution des problémes aux limites non linéaires (Dunod, Paris, 1969).Google Scholar
5. Migórski, S., A counterexample to a compact embedding theorem for functions with values in a Hilbert space, Proc. Amer. Math. Soc. 123 (1995), 2447–2450.CrossRefGoogle Scholar
6. Nagy, E. V., A theorem on compact embedding for functions with values in an infinite dimensional Hilbert space, Ann. Univ. Sci. Budapest. Eötvös Sect. Math. 22–23 (1979–1980), 243–245.Google Scholar
7. Papageorgiou, N. S., Convergence theorems for Banach space values integrable multi-functions, Internat. J. Math. Math. Sci. 10 (1987), 433–442.CrossRefGoogle Scholar
8. Papageorgiou, N. S., Optimal control of nonlinear evolution inclusions, J. Optim. Theory Appl. 67(1990), 321–354.CrossRefGoogle Scholar
9. Papageorgiou, N. S., A minimax optimal control problem for evolution inclusions, Yokohama Math. J. 39 (1991), 1–19.Google Scholar
10. Papageorgiou, N. S., Continuous dependence results for a class of evolution inclusions, Proc. Edinburgh Math. Soc. 35 (1992), 139–158.CrossRefGoogle Scholar
11. Papageorgiou, N. S., On the set of solutions of a class of nonlinear evolution inclusions, Kodai Math. J. 15 (1992), 387–402.CrossRefGoogle Scholar
12. Papageorgiou, N. S., Existence and variational problems for nonlinear evolution inclusions, Math. Japan. 38 (1993), 433–443.Google Scholar
13. Simon, J., Compact sets in the space Lp(0, T;B), Ann. Mat. Pura Appl. (4) 146 (1987), 65–96.CrossRefGoogle Scholar
14. Wagner, D., Survey of measurable selection theorems, SIAM J. Control Optim. 15 (1977), 859–903.CrossRefGoogle Scholar
15. Zeidler, E., Nonlinear Functional Analysis and its Applications II (Springer, New York, 1990).Google Scholar