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On the Cauchy problem for ordinary differential equations in Banach spaces. (English) Zbl 0496.34033

MSC:
 34G20 Nonlinear ODE in abstract spaces
Full Text:
References:
 [1] D. Amir andJ. Lindenstrauss, The structure of weakly compact sets in Banach spaces. Ann. Math. (2)88, 35--46 (1968). · Zbl 0164.14903 · doi:10.2307/1970554 [2] K.Deimling, Ordinary differential equations in Banach spaces. LNM596, Berlin-Heidelberg-New York 1977. · Zbl 0361.34050 [3] K.Deimling, On some open problems for ordinary differential equations. Equa-Diff78, Firenze 1978. · Zbl 0418.34060 [4] J.Diestel, Geometry of Banach spaces -- Selected topics. LNM485, Berlin-Heidelberg-New York 1975. · Zbl 0307.46009 [5] L. S.Goldenshtein and A. S.Markus, On the measure of noncompactness of bounded sets and linear operators, Issled. po algebre i matem. analizu, Kishinev, 45--54 (1965). [6] K.Kuratowski, Topology Vol. II. New York 1966. [7] G. Ladas andV. Lakshmikantham, Global existence and asymptotic equilibrium in Banach spaces. J. Indian Math. Soc.36, 33--40 (1972). · Zbl 0273.34040 [8] T.-Y. Li, Existence of solutions for ordinary differential equations in Banach spaces. J. Differential Equations18, 29--40 (1975). · Zbl 0325.34069 · doi:10.1016/0022-0396(75)90079-0 [9] B. N. Sadovskii, Limit-compact and condensing operators. Russian Math. Surveys27, 85--155 (1972). · Zbl 0243.47033 · doi:10.1070/RM1972v027n01ABEH001364