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Controllability for Functional Differential and Integrodifferential Inclusions in Banach Spaces

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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.

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References

  1. 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.

    Google Scholar 

  2. 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.

    Google Scholar 

  3. 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.

    Google Scholar 

  4. MARTELLI, M., A Rothe's Type Theorem for Noncompact Acyclic-Valued Map, Bollettino dell ' Unione Matematica Italiana, Vol. 11, pp. 70-76, 1975.

    Google Scholar 

  5. 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.

    Google Scholar 

  6. BENCHOHRA, M., and NTOUYAS, S. K., An Existence Result for Second-Order Functional Differential Inclusions, Results in Mathematics, Vol. 38, pp. 9-17, 2000.

    Google Scholar 

  7. YOSIDA, K., Functional Analysis, 6th Edition, Springer Verlag, Berlin, Germany, 1980.

    Google Scholar 

  8. DEIMLING, K., Multivalued Differential Equations, Walter de Gruyter, Berlin, Germany, 1992.

    Google Scholar 

  9. HU, S., and PAPAGEORGIOU, N., Handbook of Multivalued Analysis, Volume 1: Theory, Kluwer Academic Publishers, Dordrecht, Holland, 1997.

    Google Scholar 

  10. BANAS, J., and GOEBEL, K., Measures of Noncompactness in Banach Spaces, Marcel Dekker, New York, NY, 1980.

    Google Scholar 

  11. GOLDSTEIN, J. K., Semigroups of Linear Operators and Applications, Oxford University Press, New York, NY, 1985.

    Google Scholar 

  12. HEIKKILA, S., and LAKSHMIKANTHAM, V., Monotone Iterative Techniques for Discontinuous Nonlinear Differential Equations, Marcel Dekker, New York, NY, 1994.

    Google Scholar 

  13. FATTORINI, O., Second-Order Linear Differential Equations in Banach Spaces, North-Holland Mathematical Studies, North-Holland, Amsterdam, Holland, Vol. 108, 1985.

    Google Scholar 

  14. 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.

    Google Scholar 

  15. 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.

    Google Scholar 

  16. 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.

    Google Scholar 

  17. 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.

    Google Scholar 

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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

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