A Nagumo-like uniqueness result for a second order ODE

Monatshefte fur Mathematik

Volumn 168, Issue 2, 2012, Pages 273-277

  Mustafa, Octavian G ^a  

^a UNIVERSITY OF VIENNA   (Austria)

Author keywords

Non Lipschitzian functional term; Ordinary differential equation; Uniqueness of solution

Indexed keywords

EID: 84867743678     PISSN: 00269255     EISSN: None     Source Type: Journal    
DOI: 10.1007/s00605-011-0324-2     Document Type: Article

References (17)

1. Athanassov Z. S.: Uniqueness and convergence of successive approximations for ordinary differential equations. Math. Jpn. 35, 351-367 (1990).
2. Bertozzi A., Majda A.: Vorticity and incompressible flow. Cambridge University Press, Cambridge (2000).
3. Chemin J. Y., Lerner N.: Flot de champs de vecteurs non lipschitziens et équations de Navier-Stokes. J. Differ. Equ. 121, 314-328 (1995).
4. Constantin A.: On the unicity of solutions for high-order differential equations. Istituto Lombardo (Rend. Sci.) A 130, 171-181 (1996).
5. Constantin A.: The trajectories of particles in Stokes waves. Invent. Math. 166, 523-535 (2006).
6. Constantin A.: On Nagumo's theorem. Proc. Jpn. Acad. 86(A), 41-44 (2010).
7. Constantin A.: A dynamical systems approach towards isolated vorticity regions for tsunami background states. Arch. Rat. Mech. Anal. 200, 239-253 (2011).
8. Kaper H. G., Kwong M. K.: Uniqueness for a class of nonlinear initial value problems. J. Math. Anal. Appl. 130, 467-473 (1988).
9. Mejstrik, T.: Some remarks on Nagumo's theorem. Czechoslov. Math. J. (to appear).
10. Mustafa, O. G.: On the uniqueness of flow in a recent tsunami model, Applicable Analysis, accepted. http://arxiv. org/abs/1103. 2470.
11. Nagumo, M.: Eine hinreichende Bedingung für die Unität der Lösung von Differentialgleichungen erster Ordnung. Jpn. J. Math. 3, 107-112 (1926) Reprinted In: Mitio Nagumo Collected Papers, Eds. M. Yamaguti, L. Nirenberg, S. Mizohata, Y. Sibuya, Springer, Tokyo, 1993.
12. Nagumo, M.: Eine hinreichende Bedingung für die Unität der Lösung von gewöhnlichen Differentialgleichungen n-ter Ordnung, Japan J. Math. 4, 307-309 (1927) Reprinted In: Mitio Nagumo Collected Papers, Eds. M. Yamaguti, L. Nirenberg, S. Mizohata, Y. Sibuya, Springer, Tokyo, 1993.
13. Strauss, W.: Nonlinear wave equations, CBMS Regional Conference Series in Mathematics. Am. Math. Soc. Providence (1989).
14. Ni W. M., Nussbaum R.: Uniqueness and nonuniqueness for positive radial solutions of Δu + f(u, r) = 0. Commun. Pure Appl. Math. 38, 67-108 (1985).
15. n. Arch. Rat. Mech. Anal. 81, 181-197 (1983).
16. Wahlén E.: Uniqueness for autonomous planar differential equations and the Lagrangian formulation of water flows with vorticity. J. Nonlinear Math. Phys. 11, 549-555 (2004).
17. nt. Boll. Un. Mat. Ital. 11, 496-498 (1956).