Constantin, Adrian On Nagumo’s theorem. (English) Zbl 1192.34014 Proc. Japan Acad., Ser. A 86, No. 2, 41-44 (2010). Summary: We present a different perspective on Nagumo’s uniqueness theorem and its various generalizations. This allows us to improve these generalizations. Cited in 3 ReviewsCited in 16 Documents MSC: 34A12 Initial value problems, existence, uniqueness, continuous dependence and continuation of solutions to ordinary differential equations Keywords:ordinary differential equation; uniqueness × Cite Format Result Cite Review PDF Full Text: DOI References: [1] Z. S. Athanassov, Uniqueness and convergence of successive approximations for ordinary differential equations, Math. Japon 35 (1990), no. 2, 351-367. · Zbl 0709.34002 [2] R. Bellman, Stability theory of differential equations , McGraw-Hill Book Company, Inc., New York, 1953. · Zbl 0053.24705 [3] A. Constantin, On the existence of positive solutions of second order differential equations, Ann. Mat. Pura Appl. (4) 184 (2005), no. 2, 131-138. · Zbl 1223.34041 · doi:10.1007/s10231-004-0100-1 [4] A. Constantin, On the unicity of solutions for the differential equation x ( n ) ( t )= f ( t , x ), Rend. Circ. Mat. Palermo (2) 42 (1993), no. 1, 59-64. · Zbl 0796.34004 · doi:10.1007/BF02845110 [5] A. Constantin, On the existence and pathwise uniqueness of solutions of stochastic differential equations, Stochastics Stochastics Rep. 56 (1996), no. 3-4, 227-239. · Zbl 0886.60051 · doi:10.1080/17442509608834044 [6] W. A. Coppel, Stability and asymptotic behavior of differential equations , D. C. Heath and Co., Boston, Mass., 1965. · Zbl 0154.09301 [7] M. Nagumo, Eine hinreichende Bedingung für die Unität der Lösung von Differentialgleichungen erster Ordnung, Japan J. Math. 3 (1926), 107-112. · JFM 52.0438.01 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.