Abstract
In this section we recall some notions of the theory of multivalued maps (details can be found, e.g., in [13, 24, 25, 39, 56, 64, 75, 80] and other sources).
Keywords
- Banach Space
- Topological Vector Space
- Topological Degree
- Coincidence Degree
- Topological Degree Theory
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J. Appell, E. De Pascale, H.T. Nguyen, P.P. Zabreiko, Multi-valued superpositions. Dissertationes Math. CCCXLV, pp. 1–97, 1995
J.P. Aubin, H. Frankowska, Set-Valued Analysis (Birkhauser, Boston, 1990)
H. Bohnenblust, S. Karlin, On a theorem of Ville, in Contributions in the Theory of Games, vol. 1, ed. by H.W. Kuhn, A.W.Tucker (Princeton University Press, Princeton, 1950), pp. 155–160
Yu.G. Borisovich, B.D. Gelman, A.D. Myshkis, V.V. Obukhovskii, Topological methods in the theory of fixed points of multivalued mappings. Uspekhi Mat. Nauk (Russian) 35(1)(211), 59–126 (1980); English translation: Russ. Math. Surv. 35, 65–143 (1980)
Yu.G. Borisovich, B.D. Gelman, A.D. Myshkis, V.V. Obukhovskii, Introduction to the Theory of Multivalued Maps and Differential Inclusions, 2nd edn. (Librokom, Moscow, 2011) (in Russian)
Yu.G. Borisovich, Yu.E. Gliklikh, in On the Lefschetz Number for a Class of Multi-Valued Maps. Seventh Math. Summer School (Katsiveli, 1969), pp. 283–294. Izd. Akad. Nauk Ukrain. SSR (Kiev, 1970) (in Russian)
K. Borsuk, in Theory of Retracts. Monografie Mat. vol. 44 (PWN, Warszawa, 1967)
C. Castaing, M. Valadier, in Convex Analysis and Measurable Multifunctions. Lecture Notes in Mathematics, vol. 580 (Springer, Berlin, 1977)
K. Deimling, Nonlinear Functional Analysis (Springer, Berlin, 1985)
K. Deimling, Multivalued Differential Equations, in De Gruyter Series in Nonlinear Analysis and Applications, vol. 1 (Walter de Gruyter, Berlin, 1992)
A. Fryszkowski, in Fixed Point Theory for Decomposable Sets. Topological Fixed Point Theory and Its Applications, vol. 2 (Kluwer, Dordrecht, 2004)
R.E. Gaines, J.L. Mawhin, in Coincidence Degree and Nonlinear Differential Equations. Lecture Notes in Mathematics, vol. 568 (Springer, Berlin, 1977)
L. Górniewicz, in Topological Fixed Point Theory of Multivalued Mappings, 2nd edn. Topological Fixed Point Theory and Its Applications, vol. 4 (Springer, Dordrecht, 2006)
L. Górniewicz, A. Granas, W. Kryszewski, On the homotopy method in the fixed point index theory of multi-valued mappings of compact absolute neighborhood retracts. J. Math. Anal. Appl. 161(2), 457–473 (1991)
J.K. Hale, J. Kato, Phase space for retarded equations with infinite delay. Funkcial. Ekvac. 21(1), 11–41 (1978)
Y. Hino, S. Murakami, T. Naito, in Functional Differential Equations with Infinite Delay. Lecture Notes in Mathematics, vol. 1473 (Springer, Berlin, 1991)
M.W. Hirsch, in Differential Topology. Graduate Texts in Mathematics, vol. 33 (Springer, New York, 1994)
S. Hu, N.S. Papageorgiou, in Handbook of Multivalued Analysis. Vol. I. Theory. Mathematics and Its Applications, vol. 419 (Kluwer, Dordrecht, 1997)
D.M. Hyman, On decreasing sequences of compact absolute retracts. Fund. Math. 64, 91–97 (1969)
J. Jezierski, W. Marzantowicz, in Homotopy Methods in Topological Fixed and Periodic Point Theory. Topological Fixed Point Theory and Applications, vol. 2 (Springer, Dordrecht, 2006)
M. Kamenskii, V. Obukhovskii, P. Zecca, in Condensing Multivalued Maps and Semilinear Differential Inclusions in Banach Spaces. de Gruyter Series in Nonlinear Analysis and Applications, vol. 7 (Walter de Gruyter, Berlin, 2001)
M.A. Krasnosel’skii, Topological Methods in the Theory of Nonlinear Integral Equations (Gostekhizdat, Moscow, 1956) (in Russian); English translation (A Pergamon Press Book The Macmillan Co., New York, 1964)
M.A. Krasnosel’skii, P.P. Zabreiko, Geometrical Methods of Nonlinear Analysis (Nauka, Moscow, 1975); English translation: Grundlehren der Mathematischen Wissenschaften, vol. 263 (Springer, Berlin, 1984)
J. Mawhin, in Topological Degree Methods in Nonlinear Boundary Value Problems. Expository Lectures from the CBMS Regional Conference Held at Harvey Mudd College, Claremont, CA, June 9–15, 1977. CBMS Regional Conference Series in Mathematics, vol. 40 (American Mathematical Society, Providence, 1979)
A.D. Myshkis, Generalizations of the theorem on a fixed point of a dynamical system inside of a closed trajectory. Mat. Sb. 34(3), 525–540 (1954) (in Russian)
T. Pruszko, A coincidence degree for L-compact convex-valued mappings and its application to the Picard problem of orientors fields. Bull. Acad. Polon. Sci. Sér. Sci. Math. 27(11–12), 895–902 (1979/1981)
E. Tarafdar, S.K. Teo, On the existence of solutions of the equation Lx ∈ Nx and a coincidence degree theory. J. Aust. Math. Soc. Ser. A 28(2), 139–173 (1979)
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Obukhovskii, V., Zecca, P., Van Loi, N., Kornev, S. (2013). Background. In: Method of Guiding Functions in Problems of Nonlinear Analysis. Lecture Notes in Mathematics, vol 2076. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-37070-0_1
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