On ω -limit sets of nonautonomous differential equations

Boris S. Klebanov

Commentationes Mathematicae Universitatis Carolinae (1994)

  • Volume: 35, Issue: 2, page 267-281
  • ISSN: 0010-2628

Abstract

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In this paper the ω -limit behaviour of trajectories of solutions of ordinary differential equations is studied by methods of an axiomatic theory of solution spaces. We prove, under very general assumptions, semi-invariance of ω -limit sets and a Poincar’e-Bendixon type theorem.

How to cite

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Klebanov, Boris S.. "On $\omega $-limit sets of nonautonomous differential equations." Commentationes Mathematicae Universitatis Carolinae 35.2 (1994): 267-281. <http://eudml.org/doc/247598>.

@article{Klebanov1994,
abstract = {In this paper the $\omega $-limit behaviour of trajectories of solutions of ordinary differential equations is studied by methods of an axiomatic theory of solution spaces. We prove, under very general assumptions, semi-invariance of $\omega $-limit sets and a Poincar’e-Bendixon type theorem.},
author = {Klebanov, Boris S.},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {$\omega $-limit sets; stationary points; the Poincar’e-Bendixon theorem; asymptotic behaviour; nonautonomous ordinary differential equations; Poincaré-Bendixson theorem},
language = {eng},
number = {2},
pages = {267-281},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {On $\omega $-limit sets of nonautonomous differential equations},
url = {http://eudml.org/doc/247598},
volume = {35},
year = {1994},
}

TY - JOUR
AU - Klebanov, Boris S.
TI - On $\omega $-limit sets of nonautonomous differential equations
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 1994
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 35
IS - 2
SP - 267
EP - 281
AB - In this paper the $\omega $-limit behaviour of trajectories of solutions of ordinary differential equations is studied by methods of an axiomatic theory of solution spaces. We prove, under very general assumptions, semi-invariance of $\omega $-limit sets and a Poincar’e-Bendixon type theorem.
LA - eng
KW - $\omega $-limit sets; stationary points; the Poincar’e-Bendixon theorem; asymptotic behaviour; nonautonomous ordinary differential equations; Poincaré-Bendixson theorem
UR - http://eudml.org/doc/247598
ER -

References

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