Extremal solutions to a class of multivalued integral equations in Banach space.
Aizicovici, Sergiu, Papageorgiou, Nikolaos S. (1992)
Journal of Applied Mathematics and Stochastic Analysis
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Aizicovici, Sergiu, Papageorgiou, Nikolaos S. (1992)
Journal of Applied Mathematics and Stochastic Analysis
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Ahmed, N.U., Kerbal, Sebti (1993)
Journal of Applied Mathematics and Stochastic Analysis
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Papageorgiou, Nikolaos S. (1994)
Journal of Applied Mathematics and Stochastic Analysis
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Nikolaos S. Papageorgiou (1994)
Commentationes Mathematicae Universitatis Carolinae
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We consider boundary value problems for semilinear evolution inclusions. We establish the existence of extremal solutions. Using that result, we show that the evolution inclusion has periodic extremal trajectories. These results are then applied to closed loop control systems. Finally, an example of a semilinear parabolic distributed parameter control system is worked out in detail.
Nikolaos S. Papageorgiou (1993)
Mathematica Slovaca
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Nikolaos S. Papageorgiou (1997)
Czechoslovak Mathematical Journal
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In the paper we study the topological structure of the solution set of a class of nonlinear evolution inclusions. First we show that it is nonempty and compact in certain function spaces and that it depends in an upper semicontinuous way on the initial condition. Then by strengthening the hypothesis on the orientor field , we are able to show that the solution set is in fact an -set. Finally some applications to infinite dimensional control systems are also presented.