Geodesic
Jorke's Theorem and Wirtinger's Inequality
Matematičeskie zametki, Tome 70 (2001) no. 2, pp. 237-245 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

We consider autonomous systems of ordinary differential equations (of first or higher order) whose right-hand sides satisfy the Lipschitz condition stated in terms of the Euclidean metric and of nonnegative matrices. Using Wirtinger's inequality, we prove theorems on the lower bounds for the periods of periodic nonstationary solutions of autonomous systems, which generalize Jorke's theorem. In the case of nonnegative indecomposable matrices we discuss the sharpness of the estimates obtained. 
@article{MZM_2001_70_2_a7,
     author = {A. I. Perov},
     title = {Jorke's {Theorem} and {Wirtinger's} {Inequality}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {237--245},
     year = {2001},
     volume = {70},
     number = {2},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2001_70_2_a7/}
}
TY  - JOUR
AU  - A. I. Perov
TI  - Jorke's Theorem and Wirtinger's Inequality
JO  - Matematičeskie zametki
PY  - 2001
SP  - 237
EP  - 245
VL  - 70
IS  - 2
UR  - http://geodesic.mathdoc.fr/item/MZM_2001_70_2_a7/
LA  - ru
ID  - MZM_2001_70_2_a7
ER  - 
%0 Journal Article
%A A. I. Perov
%T Jorke's Theorem and Wirtinger's Inequality
%J Matematičeskie zametki
%D 2001
%P 237-245
%V 70
%N 2
%U http://geodesic.mathdoc.fr/item/MZM_2001_70_2_a7/
%G ru
%F MZM_2001_70_2_a7
A. I. Perov. Jorke's Theorem and Wirtinger's Inequality. Matematičeskie zametki, Tome 70 (2001) no. 2, pp. 237-245. http://geodesic.mathdoc.fr/item/MZM_2001_70_2_a7/

[1] Gantmakher F. R., Teoriya matrits, Nauka, M., 1967

[2] Jorke J. A., “Periods of periodic solutions and the Lipschitz constants”, Proc. Amer. Math. Soc., 22 (1964), 509–512

[3] Krasnoselskii M. A., Lifshits E. A., Sobolev A. V., Pozitivnye lineinye sistemy, Nauka, M., 1985

[4] Kryukov B. I., Vynuzhdennye kolebaniya suschestvenno nelineinykh sistem, Mashinostroenie, M., 1984

[5] Khardi G. G., Littlvud D. E., Polia G., Neravenstva, IL, M., 1948