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.
@article{118671, author = {Nikolaos S. Papageorgiou}, title = {Boundary value problems and periodic solutions for semilinear evolution inclusions}, journal = {Commentationes Mathematicae Universitatis Carolinae}, volume = {35}, year = {1994}, pages = {325-336}, zbl = {0807.34077}, mrnumber = {1286579}, language = {en}, url = {http://dml.mathdoc.fr/item/118671} }
Papageorgiou, Nikolaos S. Boundary value problems and periodic solutions for semilinear evolution inclusions. Commentationes Mathematicae Universitatis Carolinae, Tome 35 (1994) pp. 325-336. http://gdmltest.u-ga.fr/item/118671/
Nonlinear problems for systems of differential equations, Nonlinear Anal.-TMA 1 (1977), 691-699. (1977) | MR 0592963 | Zbl 0388.34011
Points Extremaux, Multi-applications et Fonctionelles Intégrales, Thèse du 3ème cycle, Université de Grenoble, 1975.
Vector Measures, Math. Surveys, Vol. 15, AMS, Providence, RI, 1977. | MR 0453964 | Zbl 0521.46035
Measurable relations, Fund. Math. 87 (1975), 57-91. (1975) | MR 0367142 | Zbl 0296.28003
Locally invertible operators and existence problems in differential systems, Tohoku Math. Jour. 28 (1976), 167-176. (1976) | MR 0430385 | Zbl 0356.34019
Theory of Correspondences, Wiley, New York, 1984. | MR 0752692 | Zbl 0556.28012
Compacité des résolvantes des opérateurs maximaux cycliquement monotones, Proc. Japan Acad. 49 (1973), 303-305. (1973) | MR 0346600 | Zbl 0272.47034
On the theory of Banach space valued multifunctions. Part 1: Integration and conditional expectation, J. Multiv. Anal. 17 (1985), 185-206. (1985) | MR 0808276
Convergence theorems for Banach space valued integrable multifunctions, Intern. J. Math. and Math. Sci. 10 (1987), 433-442. (1987) | MR 0896595 | Zbl 0619.28009
On multivalued evolution equations and differential inclusions in Banach spaces, Comm. Math. Univ. S.P. 36 (1987), 21-39. (1987) | MR 0892378 | Zbl 0641.47052
Boundary value problems for evolution inclusions, Comment. Math. Univ. Carolinae 29 (1988), 355-363. (1988) | MR 0957404 | Zbl 0696.35074
On evolution inclusion associated with time dependent convex subdifferentials, Comment. Math. Univ. Carolinae 31 (1990), 517-527. (1990) | MR 1078486
Nonlinear Evolution Operators and Semigroups, Lecture Notes in Math. 1260, Springer, Berlin, 1987. | MR 0900380 | Zbl 0626.35003
Equations in Evolution, Pitman, London, 1979.
Extreme continuous selectors of multivalued maps and the ``bang-bang'' principle for evolution inclusions, Soviet Math. Doklady 317 (1991), 481-485. (1991) | MR 1121349
Survey of measurable selection theorems, SIAM J. Control. Optim. 15 (1977), 859-903. (1977) | MR 0486391 | Zbl 0407.28006
Nonlinear boundary value problems in Banach spaces for multivalued differential equations on a non-compact interval, Nonlinear Anal.-TMA 3 (1979), 347-352. (1979) | MR 0532895