Abstract
In this paper, we establish sufficient conditions for the controllability of functional differential and integrodifferential inclusions in Banach spaces. We rely on a fixed-point theorem for condensing maps due to Martelli.
Similar content being viewed by others
References
BALACHANDRAN, K., BALASUBRAMANIAM, P., and DAUER, J. P., Controllability of Nonlinear Integrodifferential Systems in Banach Space, Journal of Optimization Theory and Applications, Vol. 74, 83-91, 1995.
BALACHANDRAN, K., BALASUBRAMANIAM, P., and DAUER, J. P., Local Null Controllability of Nonlinear Functional Differential Systems in Banach Space, Journal of Optimization Theory and Applications, Vol. 75, pp. 61-75, 1996.
HAN, H. K., and PARK, J. Y., Boundary Controllability of Differential Equations with Nonlocal Condition, Journal of Mathematical Analysis and Applications, Vol. 230, pp. 241-250, 1999.
MARTELLI, M., A Rothe's Type Theorem for Noncompact Acyclic-Valued Map, Bollettino dell ' Unione Matematica Italiana, Vol. 11, pp. 70-76, 1975.
BENCHOHRA, M., and NTOUYAS, S. K., Existence Results for Functional Differential and Integrodifferential Inclusions in Banach Spaces, Indian Journal of Pure and Applied Mathematics, Vol. 32, pp. 665-675, 2001.
BENCHOHRA, M., and NTOUYAS, S. K., An Existence Result for Second-Order Functional Differential Inclusions, Results in Mathematics, Vol. 38, pp. 9-17, 2000.
YOSIDA, K., Functional Analysis, 6th Edition, Springer Verlag, Berlin, Germany, 1980.
DEIMLING, K., Multivalued Differential Equations, Walter de Gruyter, Berlin, Germany, 1992.
HU, S., and PAPAGEORGIOU, N., Handbook of Multivalued Analysis, Volume 1: Theory, Kluwer Academic Publishers, Dordrecht, Holland, 1997.
BANAS, J., and GOEBEL, K., Measures of Noncompactness in Banach Spaces, Marcel Dekker, New York, NY, 1980.
GOLDSTEIN, J. K., Semigroups of Linear Operators and Applications, Oxford University Press, New York, NY, 1985.
HEIKKILA, S., and LAKSHMIKANTHAM, V., Monotone Iterative Techniques for Discontinuous Nonlinear Differential Equations, Marcel Dekker, New York, NY, 1994.
FATTORINI, O., Second-Order Linear Differential Equations in Banach Spaces, North-Holland Mathematical Studies, North-Holland, Amsterdam, Holland, Vol. 108, 1985.
TRAVIS, C. C., and WEBB, G. F., Second-Order Differential Equations in Banach Spaces, Proceedings of the International Symposium on Nonlinear Equations in Abstract Spaces, Academic Press, New York, NY, pp. 331-361, 1978.
TRAVIS, C. C., and WEBB, G. F., Cosine Families and Abstract Nonlinear Second-Order Differential Equations, Acta Mathematica Hungarica, Vol. 32, pp. 75-96, 1978.
CARMICHAEL, N., and QUINN, M. D., An Approach to Nonlinear Control Problems Using Fixed-Point Methods, Degree Theory, and Pseudo Inverses, Numerical Functional Analysis and Optimization, Vol. 7, pp. 197-219, 1984-1985.
LASOTA, A., and OPIAL, Z., An Application of the Kakutani-Ky-Fan Theorem in the Theory of Ordinary Differential Equations, Academic Polonaise des Sciences, Série des Sciences Mathématiques, Astronomiques et Physiques, Vol. 13, pp. 781-786, 1965.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Benchohra, M., Ntouyas, S. Controllability for Functional Differential and Integrodifferential Inclusions in Banach Spaces. Journal of Optimization Theory and Applications 113, 449–472 (2002). https://doi.org/10.1023/A:1015352503233
Issue Date:
DOI: https://doi.org/10.1023/A:1015352503233