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M. Benchohra, L. Gorniewicz, S. K. Ntouyas
Plock University Press, 2003
Plock University Press, 2003
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APA
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Benchohra, M., Gorniewicz, L., & Ntouyas, S. K. (2003). Controllability of Some Nonlinear Systems in Banach Spaces (the fixed point theory approach). Plock University Press.
Chicago/Turabian
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Benchohra, M., L. Gorniewicz, and S. K. Ntouyas. Controllability of Some Nonlinear Systems in Banach Spaces (the Fixed Point Theory Approach). Plock University Press, 2003.
MLA
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Benchohra, M., et al. Controllability of Some Nonlinear Systems in Banach Spaces (the Fixed Point Theory Approach). Plock University Press, 2003.
BibTeX Click to copy
@book{m2003a,
title = {Controllability of Some Nonlinear Systems in Banach Spaces (the fixed point theory approach)},
year = {2003},
publisher = {Plock University Press},
author = {Benchohra, M. and Gorniewicz, L. and Ntouyas, S. K.}
}
This book supplies in a certain sense the applications of fixed point theories for multivalued mappings, as developed in the monographs [L. Górniewicz, “Topological fixed point theory of multivalued mappings” (1999; Zbl 0937.55001)] and [J. Andres and L. Górniewicz, “Topological fixed point principles for boundary value problems” (2003; Zbl 1029.55002)], to optimal control problems which were considered there only occasionally.
The subject so lies in the intersection of optimal control and fixed point theories. The nonlinear systems under consideration are mostly of differential type in the ordinary sense, but functional-differential and integro-differential cases are treated as well. The equations and especially inclusions are examined in Banach spaces by which the connections with partial differential equations and inclusions (particularly of parabolic type) are available.
The book having 261 pages consists of nine chapters and an Appendix in which second-order hyperbolic differential inclusions are investigated. The headings of the single chapters reflect well the research subject:
1. Background in set-valued analysis; 2. First-order differential inclusions; 3. Second-order differential inclusions; 4. Functional-differential inclusions; 5. Neutral functional-differential inclusions; 6. Infinite time horizon problem; 7. Boundary controllability; 8. Feedback-type control problems; 9. Topological essentiality and control problems.
The character of this work is something between the monograph and the textbook.
The subject so lies in the intersection of optimal control and fixed point theories. The nonlinear systems under consideration are mostly of differential type in the ordinary sense, but functional-differential and integro-differential cases are treated as well. The equations and especially inclusions are examined in Banach spaces by which the connections with partial differential equations and inclusions (particularly of parabolic type) are available.
The book having 261 pages consists of nine chapters and an Appendix in which second-order hyperbolic differential inclusions are investigated. The headings of the single chapters reflect well the research subject:
1. Background in set-valued analysis; 2. First-order differential inclusions; 3. Second-order differential inclusions; 4. Functional-differential inclusions; 5. Neutral functional-differential inclusions; 6. Infinite time horizon problem; 7. Boundary controllability; 8. Feedback-type control problems; 9. Topological essentiality and control problems.
The character of this work is something between the monograph and the textbook.