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References
K. Borsuk, Theory of Retracts, PWN (Warsaw, 1967).
A. Bressan, A. Cellina, and A. Fryszkowski, A class of absolute retracts in spaces of integrable functions, Proc. Amer. Math. Soc., 112 (1991), 413–418.
A. Bressan and G. Colombo, Boundary value problem for lower semicontinuous differential inclusions, Funkcial. Ekvac., 36 (1993), 359–373.
A. Bressan and G. Crasta, Extremal selections of multifunctions generating a continuous flow, Ann. Polon. Math., 40 (1994), 101–117.
A. Cellina, On the set of solutions to Lipschitzian differential inclusions, Differential Integral Equations, 1 (1988), 495–500.
A. Cellina and V. Staicu, Well posedness for differential inclusions on closed sets, J. Differential Equations, 92 (1991), 2–13.
F. S. De Blaei and G. Pianigiani, A Baire category approach to the existence of solutions of multivalued differential equations in Banach spaces, Funkcial. Ekvac., 25 (1982), 153–162.
F. S. De Blasi and G. Pianigiani, Topological properties of nonconvex differential inclusions, Nonlinear Anal., 20 (1993), 871–894.
F. S. De Blasi and G. Pianigiani, On the solution sets of nonconvex differential inclusions, J. Differential Equations, to appear.
A. F. Filippov, On certain questions in the theory of optimal control, J. Soc. Indust. Appl. Math. Ser. A Control, 1 (1962), 76–94.
L. Górniewicz, S. A. Marano, and M. Slosarski, Fixed points of contractive multivalued maps, Proc. Amer. Math. Soc., 124 (1996), 2675–2683.
F. Hiai and F. Umegaki, Integrals, conditional expectations, and martingales of multivalued functions, J. Multivariate Anal., 7 (1977), 149–182.
C. J. Himmelberg, Measurable relations, Fund. Math., 87, (1975), 53–72.
K. Kuratowski and C. Ryll-Nardzewski, A general theorem on selectors, Bull. Acad. Polon. Sci. Sér. Sci. Math. Astronom. Phys., 13, (1965), 397–403.
S. A. Marano, Fixed points of multivalued contractions with nonclosed, nonconvex values, Atti Accad. Naz. Lincei Rend. Cl. Sci. Fis. Mat. Natur., 5 (1994), 203–212.
B. Ricceri, Sur l'approximation des sélections mesurables, C. R. Acad. Sci. Paris, Sér. I Math., 295 (1982), 527–530.
S. M. Robinson, Normed convex processes, Trans. Amer. Math. Soc., 174 (1972), 127–140.
V. Staicu and H. Wu, Arcwise connectedness of solution sets to Lipschitzian differential inclusions, Boll. Un. Mat. Ital., A-5 (1991), 253–256.
V. Staicu, Continuous flows of Lipschitzian differential inclusions, Preprint SISSA, 184M (1990).
V. Staicu, Continuous selections of solution sets to evolution equations, Proc. Amer. Math. Soc., 113 (1991), 403–413.
V. Staicu, Qualitative properties of solution sets to Lipschitzian differential inclusions, Proc. Int. Conf. on Differential Equations, Equadiff '91 (C. Perelló, C. Simó, and J. Solà-Morales eds), World Sci. Publ. (Singapore, 1993), pp. 910–914.
G. Wenzel, On a class of implicit differential inclusions, J. Differential Equations, 63 (1986), 162–182.
G. Wenzel, Existence of solutions for a class of implicit differential inclusions: a constructive proof, Arch. Math. (Basel), 47 (1986), 121–128.
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Marano, S., Staicu, V. On the Set of Solutions to a Class of Nonconvex Nonclosed Differential Inclusions. Acta Mathematica Hungarica 76, 287–301 (1997). https://doi.org/10.1023/A:1006533606338
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DOI: https://doi.org/10.1023/A:1006533606338