On strongly monotone flows
Annales Polonici Mathematici (1997)
- Volume: 66, Issue: 1, page 269-274
- ISSN: 0066-2216
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topWolfgang Walter. "On strongly monotone flows." Annales Polonici Mathematici 66.1 (1997): 269-274. <http://eudml.org/doc/269959>.
@article{WolfgangWalter1997,
abstract = {M. Hirsch's famous theorem on strongly monotone flows generated by autonomous systems u'(t) = f(u(t)) is generalized to the case where f depends also on t, satisfies Carathéodory hypotheses and is only locally Lipschitz continuous in u. The main result is a corresponding Comparison Theorem, where f(t,u) is quasimonotone increasing in u; it describes precisely for which components equality or strict inequality holds.},
author = {Wolfgang Walter},
journal = {Annales Polonici Mathematici},
keywords = {system of ordinary differential equations; initial value problem; comparison theorem; monotone flow; quasimonotonicity; strongly monotone flows; Carathéodory hypotheses; quasimonotone increasing},
language = {eng},
number = {1},
pages = {269-274},
title = {On strongly monotone flows},
url = {http://eudml.org/doc/269959},
volume = {66},
year = {1997},
}
TY - JOUR
AU - Wolfgang Walter
TI - On strongly monotone flows
JO - Annales Polonici Mathematici
PY - 1997
VL - 66
IS - 1
SP - 269
EP - 274
AB - M. Hirsch's famous theorem on strongly monotone flows generated by autonomous systems u'(t) = f(u(t)) is generalized to the case where f depends also on t, satisfies Carathéodory hypotheses and is only locally Lipschitz continuous in u. The main result is a corresponding Comparison Theorem, where f(t,u) is quasimonotone increasing in u; it describes precisely for which components equality or strict inequality holds.
LA - eng
KW - system of ordinary differential equations; initial value problem; comparison theorem; monotone flow; quasimonotonicity; strongly monotone flows; Carathéodory hypotheses; quasimonotone increasing
UR - http://eudml.org/doc/269959
ER -
References
top- [1] M. Hirsch, Systems of differential equations that are competitive or cooperative, II: convergence almost everywhere, SIAM J. Math. Anal. 16 (1985), 423-439. Zbl0658.34023
- [2] P. Volkmann, Gewöhnliche Differentialgleichungen mit quasimonoton wachsenden Funktionen in topologischen Vektorräumen, Math. Z. 127 (1972), 157-164. Zbl0226.34058
- [3] W. Walter, Gewöhnliche Differentialgleichungen, 5th ed., Springer, 1993.
- [4] T. Ważewski, Systèmes des équations et des inégalités différentielles ordinaires aux deuxièmes membres monotones et leurs applications, Ann. Soc. Polon. Math. 23 (1950), 112-166. Zbl0041.20705
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