Literatur
Bishop, E., Phelps, R. R.: The support functionals of a convex set. Proc. Sympos. pure Math.7 (Convexity), 27–35 (1963).
Brezis, H.: On a characterization of flow-invariant sets. Commun. pure appl. Math.23, 261–263 (1970).
Klee, V. L., Jr.: The support property of a convex set in a linear normed space. Duke math. J.15, 767–772 (1948).
Klee, V. L., Jr.: Extremal structure of convex sets. II. Math. Z.69, 90–104 (1958).
Kre\(\overset{\lower0.5em\hbox{$\smash{\scriptscriptstyle\smile}$}}{\imath } \)n, M. G., Rutman, M. A.: --Line\(\overset{\lower0.5em\hbox{$\smash{\scriptscriptstyle\smile}$}}{\imath } \)nye operatory, ostavljajuščie invariantnym konus v prostranstve Banaha. Uspehi mat. Nauk3, 3–95 (1948) [Russisch].
Redheffer, R. M.: The theorems of Bony and Brezis on flow-invariant sets. Amer. math. Monthly79, 740–747 (1972).
Redheffer, R. M., Walter, W.: Flow-invariant sets and differential inequalities in normed spaces. Eingereicht bei Applicable Analysis.
Volkmann, P.: Gewöhnliche Differentialungleichungen mit quasimonoton wachsenden Funktionen in topologischen Vektorräumen. Math. Z.127, 157–164 (1972).
Walter, W.: Ordinary differential inequalities in ordered Banach spaces. J. differential Equations9, 253–261 (1971).
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Volkmann, P. Über die Invarianz konvexer Mengen und Differentialungleichungen in einem normierten Raume. Math. Ann. 203, 201–210 (1973). https://doi.org/10.1007/BF01629254
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DOI: https://doi.org/10.1007/BF01629254