Uniqueness for nonlinear Cauchy problems in Banach spaces
HTML articles powered by AMS MathViewer
- by Jerome A. Goldstein PDF
- Proc. Amer. Math. Soc. 53 (1975), 91-95 Request permission
Abstract:
Recently Medeiros and Diaz and Weinacht have considered the question of uniqueness for the Cauchy problem for ordinary differential equations in a complex Hilbert space. The present paper extends their results to the case of equations in an arbitrary real or complex Banach space.References
- J. B. Diaz and R. J. Weinacht, On nonlinear differential equations in Hilbert spaces, Applicable Anal. 1 (1971), no. 1, 31–41. MR 282032, DOI 10.1080/00036817108839004 J. A. Donaldson and J. A. Goldstein (in preparation).
- T. M. Flett, Some applications of Zygmund’s lemma to non-linear differential equations in Banach and Hilbert spaces, Studia Math. 44 (1972), 335–344; addendum and corrigendum, ibid. 44 (1972), 649–650. MR 333385, DOI 10.4064/sm-44-4-335-344
- Jerome A. Goldstein, Groups of isometries on Orlicz spaces, Pacific J. Math. 48 (1973), 387–393. MR 390741
- Einar Hille and Ralph S. Phillips, Functional analysis and semi-groups, American Mathematical Society Colloquium Publications, Vol. 31, American Mathematical Society, Providence, R.I., 1957. rev. ed. MR 0089373
- Tosio Kato, Nonlinear semigroups and evolution equations, J. Math. Soc. Japan 19 (1967), 508–520. MR 226230, DOI 10.2969/jmsj/01940508
- L. A. Medeiros, On nonlinear differential equations in Hilbert spaces, Amer. Math. Monthly 76 (1969), 1024–1027. MR 248433, DOI 10.2307/2317128
- Oskar Perron, Eine hinreichende Bedingung für die Unität der Lösung von Differentialgleichungen erster Ordnung, Math. Z. 28 (1928), no. 1, 216–219 (German). MR 1544953, DOI 10.1007/BF01181159
- Wolfgang Walter, Differential- und Integral-Ungleichungen und ihre Anwendung bei Abschätzungs- und Eindeutigkeits-problemen, Springer Tracts in Natural Philosophy, Vol. 2, Springer-Verlag, Berlin-New York, 1964 (German). MR 0172076
Additional Information
- © Copyright 1975 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 53 (1975), 91-95
- MSC: Primary 34G05
- DOI: https://doi.org/10.1090/S0002-9939-1975-0377218-5
- MathSciNet review: 0377218