On periodic oscillations for a class of feedback control systems in Hilbert spaces

 Access to full text

 Full (PDF)

1. [1] R. Bader and W. Kryszewski, Fixed-point index for compositions of set-valued maps with proximally ∞-connected values on arbitrary ANR's, Set-Valued Anal. 2 (3) (1994), 459-480. doi: 10.1007/BF01026835 Zbl0846.55001
2. [2] V. Barbu, Nonlinear Semigroups and Differential Equations in Banach Spaces, Noordhoff International Publishing, Leyden, 1976. Zbl0328.47035
3. [3] Yu.G. Borisovich, B.D. Gel'man, A.D. Myshkis and V.V. Obukhovskii, Introduction to the Theory of Multivalued Maps and Differential inclusions, Second edition, Librokom, Moscow, 2011 (in Russian). 
4. [4] Yu.G. Borisovich, B.D. Gelman, A.D. Myshkis and V.V. Obukhovskii, Topological methods in the theory of fixed points of multivalued mappings, (Russian) Uspekhi Mat. Nauk 35 (1980), 59-126. English translation: Russian Math. Surveys 35 (1980), 65-143. doi: 10.1070/RM1980v035n01ABEH001548 
5. [5] K. Borsuk, Theory of Retracts. Monografie Matematyczne, 44, Państwowe Wydawnictwo Naukowe, Warsaw, 1967. Zbl0153.52905
6. [6] I. Ekeland and R. Temam, Convex Analysis and Variation Problems, North Holland, Amsterdam, 1979. Zbl0546.90057
7. [7] R.E. Gaines and J.L. Mawhin, Coincidence degree and nonlinear differential equations, Lecture Notes in Mathematics, no. 568, Springer-Verlag, Berlin-New York, 1977. Zbl0339.47031
8. [8] L. Górniewicz, Topological Fixed Point Theory of Multivalued Mappings, 2nd edition. Topological Fixed Point Theory and Its Applications, 4. Springer, Dordrecht, 2006. Zbl1107.55001
9. [9] L. Górniewicz, A. Granas and W. Kryszewski, On the homotopy method in the fixed point index theory of multi-valued mappings of compact absolute neighborhood retracts, J. Math. Anal. Appl. 161 (2) (1991), 457-473. doi: 10.1016/0022-247X(91)90345-Z Zbl0757.54019
10. [10] Ph. Hartman, Ordinary Differential Equations, Corrected reprint of the second (1982) edition [Birkhäuser, Boston, MA], Classics in Applied Mathematics, 38, Society for Industrial and Applied Mathematics (SIAM), Philadelphia, PA, 2002. 
11. [11] D.M. Hyman, On decreasing sequences of compact absolute retracts, Fund Math. 64 (1969), 91-97. Zbl0174.25804
12. [12] M. Kamenskii, V. Obukhovskii and P. Zecca, Condensing Multivalued Maps and Semilinear Differential Inclusions in Banach Spaces, de Gruyter Series in Nonlinear Analysis and Applications 7, Walter de Gruyter, Berlin-New York, 2001. doi: 10.1515/9783110870893 Zbl0988.34001
13. [13] N.V. Loi, Method of guiding functions for differential inclusions in a Hilbert space, Differ. Uravn. 46 (10) (2010), 1433-1443 (in Russian); English tranl.: Differ. Equat. 46 (10) (2010), 1438-1447. doi: 10.1134/S0012266110100071 
14. [14] N.V. Loi, V. Obukhovskii and P. Zecca, Non-smooth guiding functions and periodic solutions of functional differential inclusions with infinite delay in Hilbert spaces, Fixed Point Theory 13 (2) (2012), 565-582. Zbl1287.34057
15. [15] A.D. Myshkis, Generalizations of the theorem on a stationary point of a dynamical system inside a closed trajectory, (Russian) Math. Sb. 34 (1954), 525-540. 
16. [16] V. Obukhovski, P. Zecca, N.V. Loi and S. Kornev, Method of Guiding Functions in Problems of Nonlinear Analysis, Lecture Notes in Math. 2076, Springer, Berlin, 2013. doi: 10.1007/978-3-642-37070-0 Zbl1282.34003
17. [17] L. Schwartz, Cours d'Analyse 1, Second edition, Hermann, Paris, 1981.