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An existence theorem for ordinary differential equations in Banach spaces. (English) Zbl 0264.34072


MSC:

34G99 Differential equations in abstract spaces
34A12 Initial value problems, existence, uniqueness, continuous dependence and continuation of solutions to ordinary differential equations
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[1] J. Dieudonné, Deux exemples singuliers d’équations différentielles, Acta Sci. Math. Szeged 12 (1950), no. Leopoldo Fejér et Frederico Riesz LXX annos natis dedicatus, Pars B, 38 – 40 (French). · Zbl 0037.06002
[2] James A. Yorke, A continuous differential equation in Hilbert space without existence., Funkcial. Ekvac. 13 (1970), 19 – 21. · Zbl 0248.34061
[3] M. A. Krasnosel\(^{\prime}\)skiĭ and S. G. Kreĭn, Nonlocal existence theorems and uniqueness theorems for systems of ordinary differential equations, Dokl. Akad. Nauk SSSR (N.S.) 102 (1955), 13 – 16 (Russian).
[4] Constantin Corduneanu, Equazioni differenziali negli spazi di Banach, teoremi di esistenza e di prolungabilità, Atti Accad. Naz. Lincei. Rend. Cl. Sci. Fis. Mat. Nat. (8) 23 (1957), 226 – 230 (Italian). · Zbl 0084.34201
[5] Lamberto Cesari, Existence theorems for optimal solutions in Pontryagin and Lagrange problems, J. Soc. Indust. Appl. Math. Ser. A Control 3 (1965), 475 – 498. · Zbl 0137.08204
[6] A. Lasota and C. Olech, On Cesari’s semicontinuity condition for set valued mappings, Bull. Acad. Polon. Sci. Sér. Sci. Math. Astronom. Phys. 16 (1968), 711 – 716 (English, with Loose Russian summary). · Zbl 0169.12402
[7] B. J. Pettis, A note on regular Banach spaces, Bull. Amer. Math. Soc. 44 (1938), 420-428. · Zbl 0019.12202
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