Some remarks on Nagumo's theorem
Czechoslovak Mathematical Journal, Tome 62 (2012) no. 1, pp. 235-242.

Voir la notice de l'article dans Czech Digital Mathematics Library

We provide a simpler proof for a recent generalization of Nagumo's uniqueness theorem by A. Constantin: On Nagumo's theorem. Proc. Japan Acad., Ser. A 86 (2010), 41–44, for the differential equation $x'=f(t,x)$, $ x(0)=0$ and we show that not only is the solution unique but the Picard successive approximations converge to the unique solution. The proof is based on an approach that was developed in Z. S. Athanassov: Uniqueness and convergence of successive approximations for ordinary differential equations. Math. Jap. 35 (1990), 351–367. Some classical existence and uniqueness results for initial-value problems for ordinary differential equations are particular cases of our result.
DOI : 10.1007/s10587-012-0008-7
Classification : 34A12, 34A34, 34A45
Mots-clés : ordinary differential equation; uniqueness 
@article{10_1007_s10587_012_0008_7,
     author = {Mejstrik, Thomas},
     title = {Some remarks on {Nagumo's} theorem},
     journal = {Czechoslovak Mathematical Journal},
     pages = {235--242},
     publisher = {mathdoc},
     volume = {62},
     number = {1},
     year = {2012},
     doi = {10.1007/s10587-012-0008-7},
     mrnumber = {2899747},
     zbl = {1249.34021},
     language = {en},
     url = {https://geodesic-test.mathdoc.fr/articles/10.1007/s10587-012-0008-7/}
}
TY  - JOUR
AU  - Mejstrik, Thomas
TI  - Some remarks on Nagumo's theorem
JO  - Czechoslovak Mathematical Journal
PY  - 2012
SP  - 235
EP  - 242
VL  - 62
IS  - 1
PB  - mathdoc
UR  - https://geodesic-test.mathdoc.fr/articles/10.1007/s10587-012-0008-7/
DO  - 10.1007/s10587-012-0008-7
LA  - en
ID  - 10_1007_s10587_012_0008_7
ER  - 
%0 Journal Article
%A Mejstrik, Thomas
%T Some remarks on Nagumo's theorem
%J Czechoslovak Mathematical Journal
%D 2012
%P 235-242
%V 62
%N 1
%I mathdoc
%U https://geodesic-test.mathdoc.fr/articles/10.1007/s10587-012-0008-7/
%R 10.1007/s10587-012-0008-7
%G en
%F 10_1007_s10587_012_0008_7
Mejstrik, Thomas. Some remarks on Nagumo's theorem. Czechoslovak Mathematical Journal, Tome 62 (2012) no. 1, pp. 235-242. doi : 10.1007/s10587-012-0008-7. https://geodesic-test.mathdoc.fr/articles/10.1007/s10587-012-0008-7/

Cité par Sources :