Differential inclusions - the theory initiated by Cracow Mathematical School
Abstract
Annual Lecture dedicated to the memory of Professor Andrzej Lasota.
Keywords
differential inclusions; set-valued mappings; topological fixed point theory
References
1. Andres J., Górniewicz L., Topological Fixed Point Principles for Boundary Value Problems, Kluwer Academic Publishers, 2003.
2. Aubin J.P., Cellina A., Differential Inclusions, Springer-Verlag, Berlin, 1984.
3. Aubin J.P., Frankowska H., Set-Valued Analysis, Birkhäuser, Basel, 1990.
4. Cellina A., Lasota A., A new approach to the definition of topological degree for multivalued mappings, Atti. Accad. Naz. Lincei Cl. Sci. Fis. Mat. Natur. Rend. Lincei 8 (1969), 434–440.
5. Chow S.N., Lasota A., On boundary value problems for ordinary differential equations, J. Diff. Equations 14 (1973), 326–337.
6. Deimling K., Multivalued Differential Equations, W. De Gruyter, Berlin, 1992.
7. Fryszkowski A., Fixed Point Theory for Decomposable Sets, Kluwer Academic Publisher, 2004.
8. Górniewicz L., Topological Fixed Point Theory of Multivalued Mappings, Springer-Verlag, Berlin, 2006.
9. Kamenskii M.I., Obukovskii V.V., Zecca P., Condensing Multivalued Maps and Semilinear Differential Inclusions in Banach Spaces, W. De Gruyter, Berlin, 2001.
10. Kisielewicz M., Differential Inclusions and Optimal Control, Polish Sc. Publishers and Kluwer Academic Publishers, Dordrecht, 1991.
11. Lasota A., Une generalisation du premier theoreme de Fredholm et ses applications a la theorie des equations differentielles ordinarires, Ann. Polon. Math. 18 (1966), 65–77.
12. Lasota A., Contingent equations and boundary value problems, reprint (1967), 257–266.
13. Lasota A., Applications of generalized functions to contingent equations and control theory, in: Inst. Dynamics Appl. Math. Lecture vol. 51, Univ. of Maryland, 1970–1971, pp. 41–52.
14. Lasota A., On the existence and uniqueness of solutions of a multipoint boundary value problem, Ann. Polon. Math. 38 (1980), 205–310.
15. Lasota A., Myjak J., Attractors of multifunctions, Bull. Polish Acad. Sci. Math. 48 (2000), 319–334.
16. Lasota A., Olech Cz., On the closedness of the set of trajectories of a control system, Bull. Acad. Polon. Sci. 214 (1966), 615–621.
17. Lasota A., Olech Cz., An optimal solution of Nicoletti’s boundary value problem, Ann. Polon. Math. 18 (1966), 131–139.
18. Lasota A., Opial Z., An application of the Kakutani–Ky Fan theorem in the theory of ordinary differential equations, Bull. Acad. Polon. Sci. 13 (1965), 781–786.
19. Lasota A., Opial Z., Sur la dependance conitue des solutions des equations differentielles ordinaries de leurs secondo members et des coditions aux limites, Ann. Polon. Math. 19 (1967), 13–36.
20. Lasota A., Opial Z., On the existence and uniquenness of solutions of a bondary value problem for an ordinary second order differentia equations, Coll. Math. 18 (1967), 1–5.
21. Lasota A., Opial Z., Fixed point theorem for multivalued mappings and optimal control problems, Bull. Acad. Polon. Sci. 16 (1968), 645–649.
22. Tolstonogov A.A., Differential Inclusions in Banach Spaces (in Russsian), Sc. Acad. of Sciences, Siberian Branch, Novosibirsk, 1986.
2. Aubin J.P., Cellina A., Differential Inclusions, Springer-Verlag, Berlin, 1984.
3. Aubin J.P., Frankowska H., Set-Valued Analysis, Birkhäuser, Basel, 1990.
4. Cellina A., Lasota A., A new approach to the definition of topological degree for multivalued mappings, Atti. Accad. Naz. Lincei Cl. Sci. Fis. Mat. Natur. Rend. Lincei 8 (1969), 434–440.
5. Chow S.N., Lasota A., On boundary value problems for ordinary differential equations, J. Diff. Equations 14 (1973), 326–337.
6. Deimling K., Multivalued Differential Equations, W. De Gruyter, Berlin, 1992.
7. Fryszkowski A., Fixed Point Theory for Decomposable Sets, Kluwer Academic Publisher, 2004.
8. Górniewicz L., Topological Fixed Point Theory of Multivalued Mappings, Springer-Verlag, Berlin, 2006.
9. Kamenskii M.I., Obukovskii V.V., Zecca P., Condensing Multivalued Maps and Semilinear Differential Inclusions in Banach Spaces, W. De Gruyter, Berlin, 2001.
10. Kisielewicz M., Differential Inclusions and Optimal Control, Polish Sc. Publishers and Kluwer Academic Publishers, Dordrecht, 1991.
11. Lasota A., Une generalisation du premier theoreme de Fredholm et ses applications a la theorie des equations differentielles ordinarires, Ann. Polon. Math. 18 (1966), 65–77.
12. Lasota A., Contingent equations and boundary value problems, reprint (1967), 257–266.
13. Lasota A., Applications of generalized functions to contingent equations and control theory, in: Inst. Dynamics Appl. Math. Lecture vol. 51, Univ. of Maryland, 1970–1971, pp. 41–52.
14. Lasota A., On the existence and uniqueness of solutions of a multipoint boundary value problem, Ann. Polon. Math. 38 (1980), 205–310.
15. Lasota A., Myjak J., Attractors of multifunctions, Bull. Polish Acad. Sci. Math. 48 (2000), 319–334.
16. Lasota A., Olech Cz., On the closedness of the set of trajectories of a control system, Bull. Acad. Polon. Sci. 214 (1966), 615–621.
17. Lasota A., Olech Cz., An optimal solution of Nicoletti’s boundary value problem, Ann. Polon. Math. 18 (1966), 131–139.
18. Lasota A., Opial Z., An application of the Kakutani–Ky Fan theorem in the theory of ordinary differential equations, Bull. Acad. Polon. Sci. 13 (1965), 781–786.
19. Lasota A., Opial Z., Sur la dependance conitue des solutions des equations differentielles ordinaries de leurs secondo members et des coditions aux limites, Ann. Polon. Math. 19 (1967), 13–36.
20. Lasota A., Opial Z., On the existence and uniquenness of solutions of a bondary value problem for an ordinary second order differentia equations, Coll. Math. 18 (1967), 1–5.
21. Lasota A., Opial Z., Fixed point theorem for multivalued mappings and optimal control problems, Bull. Acad. Polon. Sci. 16 (1968), 645–649.
22. Tolstonogov A.A., Differential Inclusions in Banach Spaces (in Russsian), Sc. Acad. of Sciences, Siberian Branch, Novosibirsk, 1986.
GórniewiczL. (2011). Differential inclusions - the theory initiated by Cracow Mathematical School. Annales Mathematicae Silesianae, 25, 7-25. Retrieved from https://journals.us.edu.pl/index.php/AMSIL/article/view/14018
Lech Górniewicz
gorn@mat.uni.torun.pl
Centrum Badań Nieliniowych im. Juliusza Pawła Schaudera, Uniwersytet Mikołaja Kopernika w Toruniu & Instytut Matematyki, Uniwersytet Kazimierza Wielkiego w Bydgoszczy Poland
Centrum Badań Nieliniowych im. Juliusza Pawła Schaudera, Uniwersytet Mikołaja Kopernika w Toruniu & Instytut Matematyki, Uniwersytet Kazimierza Wielkiego w Bydgoszczy Poland
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