Controllability for systems governed by semilinear differential inclusions in a Banach space with a noncompact semigroup

Nonlinear Analysis, Theory, Methods and Applications

Volumn 70, Issue 9, 2009, Pages 3424-3436

  Obukhovski, Valeri ^a   Zecca, Pietro ^a  

^a VORONEZH STATE UNIVERSITY   (Russian Federation)

Author keywords

Banach space; Condensing map; Controllability; Fixed point; Measure of noncompactness; Mild solution; Multivalued map; Semilinear differential inclusion; Topological degree

Indexed keywords

BANACH SPACES; DIFFERENTIAL EQUATIONS; INCLUSIONS; MATHEMATICAL OPERATORS; TOPOLOGY; TREES (MATHEMATICS); WAVE EQUATIONS;

CONDENSING MAP; FIXED POINT; MEASURE OF NONCOMPACTNESS; MILD SOLUTION; MULTIVALUED MAP; SEMILINEAR DIFFERENTIAL INCLUSION; TOPOLOGICAL DEGREE;

CONTROLLABILITY;

EID: 61349101442     PISSN: 0362546X     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.na.2008.05.009     Document Type: Article

References (24)

1. Akhmerov R.R., Kamenskii M.I., Potapov A.S., Rodkina A.E., and Sadovskii B.N. Measures of Noncompactness and Condensing Operators (1992), Birkhäuser, Boston, Basel, Berlin
2. Balachandran K., and Dauer J.P. Controllability of nonlinear systems in Banach spaces: A survey. J. Optim. Theory Appl. 115 1 (2002) 7-28
3. Benchohra M., Górniewicz L., and Ntouyas S.K. Controllability on infinite time horizon for first and second order functional differential inclusions in Banach spaces. Discuss. Math. Differ. Incl. Control Optim. 21 2 (2001) 261-282
4. Benchohra M., Górniewicz L., and Ntouyas S.K. Controllability of neutral functional differential and integrodifferential inclusions in Banach spaces with nonlocal conditions. Nonlinear Anal. Forum 7 1 (2002) 39-54
5. Benchohra M., Górniewicz L., Ntouyas S.K., and Ouahab A. Controllability results for impulsive functional differential inclusions. Rep. Math. Phys. 54 2 (2004) 211-228
6. Benchohra M., and Ntouyas S.K. Controllability for functional differential and integrodifferential inclusions in Banach spaces. J. Optim. Theory Appl. 113 3 (2002) 449-472
7. Benchohra M., and Ouahab A. Controllability results for functional semilinear differential inclusions in Frechet spaces. Nonlinear Anal. 61 3 (2005) 405-423
8. Borisovich Yu.G., Gelman B.D., Myshkis A.D., and Obuhovskii V.V. Topological methods in the theory of fixed points of multivalued mappings. Uspekhi Mat. Nauk 35 (1) 211 (1980) 59-126 (in Russian); English transl. Russian Math. Surveys 35 (1980) 65-143
9. Borisovich Yu.G., Gelman B.D., Myshkis A.D., and Obukhovskii V.V. Introduction to Theory of Multivalued Maps and Differential Inclusions (2005), KomKniga, Moscow (in Russian)
10. Borisovich Yu.G., and Obukhovskii V.V. On an optimization problem for control systems of parabolic type. Tr. Mat. Inst. Steklov. 211 (1995) Optim. Upr. i Differ. Uravn., 95-101 (in Russian); English transl. Proc. Steklov Inst. Math. 211 (1995), 85-91
11. Chang Y.K., and Li W.T. Controllability of functional integro-differential inclusions with an unbounded delay. J. Optim. Theory Appl. 132 1 (2007) 125-142
12. Chang Y.K., Li W.T., and Nieto J.J. Controllability of evolution differential inclusions in Banach spaces. Nonlinear Anal. 67 2 (2007) 623-632
13. Deimling K. Multivalued Differential Equations. de Gruyter Series in Nonlinear Analysis and Applications vol. 1 (1992), Walter de Gruyter, Berlin
14. Engel K.-J., and Nagel R. One-Parameter Semigroups for Linear Evolution Equations. Graduate Texts in Mathematics vol. 194 (2000), Springer-Verlag, New York
15. Górniewicz L., Ntouyas S.K., and O'Regan D. Controllability of semilinear differential equations and inclusions via semigroup theory in Banach spaces. Rep. Math. Phys. 56 3 (2005) 437-470
16. Górniewicz L., Ntouyas S.K., and O'Regan D. Controllability results for first and second order evolution inclusions with nonlocal conditions. Ann. Polon. Math. 89 1 (2006) 65-101
17. Górniewicz L., Ntouyas S.K., and O'Regan D. Existence and controllability results for first- and second-order functional semilinear differential inclusions with nonlocal conditions. Numer. Funct. Anal. Optim. 28 1-2 (2007) 53-82
18. Górniewicz L., Ntouyas S.K., and O'Regan D. Controllability of evolution inclusions in Banach spaces with nonlocal conditions. Nonlinear Anal. Forum 12 1 (2007) 103-117
19. Kamenskii M., Obukhovskii V., and Zecca P. Condensing Multivalued Maps and Semilinear Differential Inclusions in Banach Spaces. de Gruyter Series in Nonlinear Analysis and Applications vol. 7 (2001), Walter de Gruyter, Berlin, New York
20. Liu B. Controllability of impulsive neutral functional differential inclusions with infinite delay. Nonlinear Anal. 60 8 (2005) 1533-1552
21. Obukhovskii V.V. On some fixed point principles for multivalued condensing operators. Trudy Mat. Fac. Voronezh Univ. 4 (1971) 70-79 (in Russian)
22. Quinn M.D., and Carmichael N. An approach to nonlinear control problems using fixed-point methods, degree theory and pseudo-inverses. Numer. Funct. Anal. Optim. 7 2-3 (1984/85) 197-219
23. Triggiani R. A note on the lack of exact controllability for mild solutions in Banach spaces. SIAM J. Control Optim. 15 3 (1977) 407-411
24. Triggiani R. Addendum: "A note on the lack of exact controllability for mild solutions in Banach spaces". SIAM J. Control Optim. 18 1 (1980) 98-99