Martin, R. H. jun. Differential equations on closed subsets of a Banach space. (English) Zbl 0293.34092 Trans. Am. Math. Soc. 179, 399-414 (1973). Page: −5 −4 −3 −2 −1 ±0 +1 +2 +3 +4 +5 Show Scanned Page Cited in 5 ReviewsCited in 112 Documents MSC: 34G99 Differential equations in abstract spaces 47E05 General theory of ordinary differential operators × Cite Format Result Cite Review PDF Full Text: DOI References: [1] Jean-Michel Bony, Principe du maximum, inégalite de Harnack et unicité du problème de Cauchy pour les opérateurs elliptiques dégénérés, Ann. Inst. Fourier (Grenoble) 19 (1969), no. fasc. 1, 277 – 304 xii (French, with English summary). · Zbl 0176.09703 [2] Haïm Brezis, On a characterization of flow-invariant sets, Comm. Pure Appl. Math. 23 (1970), 261 – 263. · Zbl 0191.38703 · doi:10.1002/cpa.3160230211 [3] Felix E. Browder, Nonlinear mappings of nonexpansive and accretive type in Banach spaces., Bull. Amer. Math. Soc. 73 (1967), 875 – 882. · Zbl 0176.45302 [4] Felix E. Browder, Nonlinear operators and nonlinear equations of evolution in Banach spaces, Nonlinear functional analysis (Proc. Sympos. Pure Math., Vol. XVIII, Part 2, Chicago, Ill., 1968) Amer. Math. Soc., Providence, R. I., 1976, pp. 1 – 308. [5] Michael G. Crandall, Differential equations on convex sets, J. Math. Soc. Japan 22 (1970), 443 – 455. · Zbl 0224.34006 · doi:10.2969/jmsj/02240443 [6] -, A generalization of Peano’s theorem and flow invariance, Math. Res. Center Report #1228, University of Wisconsin, Madison, Wis., 1972. · Zbl 0271.34084 [7] M. G. Crandall and T. M. Liggett, Generation of semi-groups of nonlinear transformations on general Banach spaces, Amer. J. Math. 93 (1971), 265 – 298. · Zbl 0226.47038 · doi:10.2307/2373376 [8] Philip Hartman, On invariant sets and on a theorem of Ważewski, Proc. Amer. Math. Soc. 32 (1972), 511 – 520. · Zbl 0272.34049 [9] J. V. Herod, A pairing of a class of evolution systems with a class of generators., Trans. Amer. Math. Soc. 157 (1971), 247 – 260. · Zbl 0217.43702 [10] Tosio Kato, Nonlinear semigroups and evolution equations, J. Math. Soc. Japan 19 (1967), 508 – 520. · Zbl 0163.38303 · doi:10.2969/jmsj/01940508 [11] Tosio Kato, Accretive operators and nonlinear evolution equations in Banach spaces., Nonlinear Functional Analysis (Proc. Sympos. Pure Math., Vol. XVIII, Part 1, Chicago, Ill., 1968) Amer. Math. Soc., Providence, R.I., 1970, pp. 138 – 161. [12] David Lowell Lovelady and Robert H. Martin Jr., A global existence theorem for a nonautonomous differential equation in a Banach space, Proc. Amer. Math. Soc. 35 (1972), 445 – 449. · Zbl 0222.34059 [13] Robert H. Martin Jr., The logarithmic derivative and equations of evolution in a Banach space, J. Math. Soc. Japan 22 (1970), 411 – 429. · Zbl 0199.47003 · doi:10.2969/jmsj/02230411 [14] R. H. Martin Jr., A global existence theorem for autonomous differential equations in a Banach space, Proc. Amer. Math. Soc. 26 (1970), 307 – 314. · Zbl 0202.10103 [15] R. M. Redheffer, The theorems of Bony and Brezis on flow-invariant sets, Amer. Math. Monthly 79 (1972), 740 – 747. · Zbl 0278.34039 · doi:10.2307/2316263 [16] G. F. Webb, Nonlinear evolution equations and product integration in Banach spaces., Trans. Amer. Math. Soc. 148 (1970), 273 – 282. · Zbl 0199.20703 [17] G. F. Webb, Nonlinear evolution equations and product stable operators on Banach spaces, Trans. Amer. Math. Soc. 155 (1971), 409 – 426. · Zbl 0213.41104 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. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.