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


34G99 Differential equations in abstract spaces
34A12 Initial value problems, existence, uniqueness, continuous dependence and continuation of solutions to ordinary differential equations
Full Text: DOI


[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
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.