Hostname: page-component-7479d7b7d-wxhwt Total loading time: 0 Render date: 2024-07-08T23:28:52.936Z Has data issue: false hasContentIssue false
  • English
  • Français

Uniformly monotone dynamical systems

Published online by Cambridge University Press:  14 November 2011

Nikolai S. Nadirashvili
Nikolai S. Nadirashvili
Affiliation:
Fakultat für Mathematik, Universität Bielfield, Universitätstrase, Postfach 8640, 4800 Bielfield 1, Germany
Get access Rights & Permissions [Opens in a new window]

Synopsis

We present a geometric approach for systems of ordinary differential equations which generate an order preserving flow. One of our main goals is to describe qualitatively the asymptotic behaviour of trajectories of dynamical systems enjoying a uniformly monotone principle.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 123 , Issue 1 , 1993 , pp. 59 - 74
Copyright
Copyright © Royal Society of Edinburgh 1993

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

1Smith, H. L.. Systems of ordinary differential equations which generates an order preserving flow. A survey of results. SIAM Review 30 (1988), 87–113.CrossRefGoogle Scholar
2Müller, M.. Über das Fundamentaltheorem in der Theorie der gewöhnlichen Differentialgleichungen. Math. Zeit. 26 (1926), 319–355.Google Scholar
3Kamke, E.. Zur Theorie der Systeme gewöhnlicher Differentialgleichungen II. Acta Math. 58 (1932), 57–85.CrossRefGoogle Scholar
4Hirsch, M. W.. The dynamical systems approach to differential equations. Bull. Amer. Math. Soc. 11 (1984), 1–64.CrossRefGoogle Scholar
5Hirsch, M. W.. Systems of differential equations that are competitive or cooperative II, Convergence almost everywhere. SIAM. J. Math. Anal. 16 (1985), 423–439.CrossRefGoogle Scholar
6Hirsch, M. W.. Stability and convergence in strongly monotone systems. J. Reine Angew. Math. 383 (1988), 1–53.Google Scholar
7Hirsch, M. W.. Systems of differential equations which are competitive or cooperative, III. Competing species. Nonlinearity 1 (1988), 51–71.CrossRefGoogle Scholar
8Nadirashvili, N. S.. Les systèmes dynamiques uniformément monotones. C. R. Acad. Sci. Paris Sér. I Math. 312 (1991), 739–741.Google Scholar
9Nadirashvili, N. S.. On the dynamics of nonlinear parabolic equations. Dokl. Acad. Nauk USSR 309 (1989) (N6); Soviet Math. Dokl. 40 (1990) (N3), 636–639.Google Scholar
10Landis, E. M. and Nadirashvili, N. S.. Positive solutions of second order elliptic equations in unbounded domains. Mat. Sb. 126 (1985) (1); Math. USSR Sbornik 54 (1986) (1), 129–134.Google Scholar