Proceedings of the Japan Academy, Series A, Mathematical Sciences

On Nagumo's theorem

Adrian Constantin

Source: Proc. Japan Acad. Ser. A Math. Sci. Volume 86, Number 2 (2010), 41-44.

Abstract

We present a different perspective on Nagumo's uniqueness theorem and its various generalizations. This allows us to improve these generalizations.

Primary Subjects: 34A12
Secondary Subjects: 45G10, 47J05

Full-text: Open access

Links and Identifiers

Permanent link to this document: http://projecteuclid.org/euclid.pja/1265033221
Digital Object Identifier: doi:10.3792/pjaa.86.41
Zentralblatt MATH identifier: 05690874
Mathematical Reviews number (MathSciNet): MR2590189

References

[1]Z. S. Athanassov, Uniqueness and convergence of successive approximations for ordinary differential equations, Math. Japon 35 (1990), no. 2, 351-367.
Mathematical Reviews (MathSciNet): MR1049101
Zentralblatt MATH: 0709.34002
[2]R. Bellman, Stability theory of differential equations, McGraw-Hill Book Company, Inc., New York, 1953.
Mathematical Reviews (MathSciNet): MR61235
[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.
Mathematical Reviews (MathSciNet): MR2149089
Digital Object Identifier: 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.
Mathematical Reviews (MathSciNet): MR1244738
Zentralblatt MATH: 0796.34004
Digital Object Identifier: 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.
Mathematical Reviews (MathSciNet): MR1396762
Zentralblatt MATH: 0886.60051
[6]W. A. Coppel, Stability and asymptotic behavior of differential equations, D. C. Heath and Co., Boston, Mass., 1965.
Mathematical Reviews (MathSciNet): MR190463
Zentralblatt MATH: 0154.09301
[7]M. Nagumo, Eine hinreichende Bedingung für die Unität der Lösung von Differentialgleichungen erster Ordnung, Japan J. Math. 3 (1926), 107-112.

2010 © The Japan Academy

Proceedings of the Japan Academy, Series A, Mathematical Sciences

Proceedings of the Japan Academy, Series A, Mathematical Sciences