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References
Antosiewicz, H. and Cellina, A., Continuous selections and differential relations, J. Diff. Eqs. 19(1975), 386–399.
Aumann, R.J., Integrals of set-valued functions, J. Math. Anal. Appl., 12(1965), 1–12.
Artstein, Z., Yet another proof of Lyapunov convexity theorem, to appear in Proc. Amer. Math. Soc.
Blackwell, D., The range of certain vector integrals, Proc. Amer. Math. Soc. 2(1951), 390–395.
Bressan, A., Colombo, G., Extensions and selections of maps with decomposable values, Studia Mathematica 40 (1988) 69–86.
Castaing, C., Valadier, M. Convex analysis and measurable multifunctions, Lecture Notes in Math., 580, Springer Verlag Berlin 1977.
Etienne, J. Sur une demonstration du "bang-bang" principle, Bull.Soc.Roy.Sci. liege 11/12(1968), 551–556.
Frankowska, H., Olech, C., R-convexity of the integral of set-valued functions, Contributions to analysis and geometry, Johns Hopkins University Press, Baltimore, 1981, 117–129.
Fryszkowski, A. Continuous selections for a class of non-convex multivalued maps. Studia Math., 76(1983), 163–174.
Halkin, H., Some further generalization of a theorem of Lyapounov, Arch. Rational Mech.Anal. 17(1964), 272–277.
Halkin, H., Hendricks E.C., Sub-integrals of set-valued function with semianalytic graphs., Proc. Nat. Acad. Sci. 59(1968) 365–367.
Halmos, P.R., The range of a vector measure, Bull.Amer.Math. Soc., 54(1948), 416–421.
Hermes, H., LaSalle, J.P., Functional analysis and time optimal control, Mathematics in science nad engineering 56(1969).
Kaczyński, H., Olech, C., Existence of solutions of orientor fields with nonconvex right-hand side, Annal.Polon.Math., 29(1974), 61–66.
Karafiat, A., On the continuity of a mapping inverse to a vector measure, Commentationes Mathematicae, 18(1974/76) 37–43.
Kingman, J.F.C., Robertson A.P., On a theorem of Lyapounov, J. London Math Soc. 43(1968), 347–351.
LaSalle, J.P., The time optimal control problem. Contr. to the theory of non linear oscilations. Princeton Univ. Press. Princeto 1960
Lyapunov, A.A., Sur le fonction-vecteurs comletement additives, Izv.Akad.Nauk.S.S.S.R. Ser. Mat. 4(1940), 465–478
Lyapunov, A.A., Sur le fonction-vecteurs comletement additives II, Izv.Akad.Nauk.S.S.S.R. Ser. Mat. 10(1946) 277–279
Linderstrauss, J. A short proof of Liapounoff's convexity theorem, J. Math. and Mech. 15(1966) 971–972.
Neustadt, L.W., The existence of optimal control in the absence of convexity conditions, J.Math.Anal.Appl. 7(1963), 110–117.
Olech, C., A contribution to the time optimal control problem, III. Konferenz uber nichtlineare Schwingungen, Teill II, Academie-Verlag-Berlin 1966, 438–446.
Olech, C., Extremal solutions of a control system, Journal of Diff. Equations, 2(1966), 74–101.
Olech, C., Lexicografical order, range of integrals and "bang-bang" principle Mathematical Theory of Control, Academic Press New York and London 1967, 35–45.
Olech, C., On the range of an unbounded vector-valued measure, Math. System Theory, 2(1968), 251–256.
Olech, C., Integrals of set-valued functions and optimal control problems, IFAC, Warszawa 1969.
Olech, C., Integrals of set-valued functions and optimal control problems, Colloque sur la Theorie Mathematique du Controle Optimale. Vander. Louvain — Belgique — 1970, 109–125.
Olech, C., Existence theory in optimal control, in Control Theory and Topics in Functional Analysis, International Atomic Energy Agency, Vienna 1976, Vol. I, 291–328.
Olech, C., Existence of solutions of non convex orientor fields, Boll. Un. Mat.Ital.Serie IV, 11(1975), 189–197.
Olech, C., Decomposability as substitute for convexity, Lecture Notes in Mathematics 1091, Springer-Verlag 1984, 193–205.
Olech, C., On n-dimensional extensions of Fatou's lemma, J. of Applied Mathematics and Physics (ZAMP) 38(1987), 266–272.
Rzeżuchowski, T., Strong convergence of selections implied by weak; applications to differential and control systems, (to appear).
Visintin, A., Strong convergence results related to strict convexity, Comm.Part.Diff.Eqs., 9(1984), 439–466.
Ważewski, T. On an optimal control problem, Proc. Conf. Diff. Equ. and their applic. (1964), 229–242.
Yorke, J.A. Another proof of Lyapounov convexity theorem, SIAM J. Control 9(1971), 351–353.
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Olech, C. (1990). The Lyapunov Theorem: Its extensions and applications. In: Cellina, A. (eds) Methods of Nonconvex Analysis. Lecture Notes in Mathematics, vol 1446. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0084932
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