Existence of unstable sets for invariant sets in compact semiflows. Applications in order-preserving semiflows

Peter Poláčik

Commentationes Mathematicae Universitatis Carolinae (1990)

  • Volume: 031, Issue: 2, page 263-276
  • ISSN: 0010-2628

How to cite

top

Poláčik, Peter. "Existence of unstable sets for invariant sets in compact semiflows. Applications in order-preserving semiflows." Commentationes Mathematicae Universitatis Carolinae 031.2 (1990): 263-276. <http://eudml.org/doc/17844>.

@article{Poláčik1990,
author = {Poláčik, Peter},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {semiflow; invariant set; limit set; order preserving},
language = {eng},
number = {2},
pages = {263-276},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {Existence of unstable sets for invariant sets in compact semiflows. Applications in order-preserving semiflows},
url = {http://eudml.org/doc/17844},
volume = {031},
year = {1990},
}

TY - JOUR
AU - Poláčik, Peter
TI - Existence of unstable sets for invariant sets in compact semiflows. Applications in order-preserving semiflows
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 1990
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 031
IS - 2
SP - 263
EP - 276
LA - eng
KW - semiflow; invariant set; limit set; order preserving
UR - http://eudml.org/doc/17844
ER -

References

top
  1. N. D. Alikakos P. Hess H. Matano, Discrete order preserving semigroups and stability for periodic parabolic differential equations, preprint. MR1027972
  2. J. K. Hale, Theory of Functional Differential Equations, Springer-Verlag, New York 1977. (1977) Zbl0352.34001MR0508721
  3. J. K. Hale, Asymptotic Behaviour of Dissipative Systems, AMS Publications, Providence 1988. (1988) MR0941371
  4. P. Hess, On stabilization of discrete strongly order-preserving semigroups and dynamical processes, Proceedings of Trends in Semigroup Theory and Applications, M. Dekker (ed.), to appear. MR1009399
  5. M. W. Hirsch, Systems of differential equations that are competitive or cooperative. I: Limit sets, SIAM J. Math. Anal. 13 (1982), 167-179. (1982) MR0647119
  6. M. W. Hirsch, Systems of differential equations that are competitive or cooperative. II: Convergence almost everywhere, SIAM J. Math. Anal. 16 (1985), 423-439. (1985) Zbl0658.34023MR0783970
  7. M. W. Hirsch, Systems of differential equations that are competitive or cooperative. III: Competing species, Nonlinearity 1 (1988), 51-71. (1988) MR0928948
  8. M. W. Hirsch, The dynamical systems approach to differential equations, Bull. AMS 11 (1984), 1-64. (1984) Zbl0541.34026MR0741723
  9. M. W. Hirsch, Differential equations and convergence almost everywhere in strongly monotone flows, Contemporary Math. 17, Providence 1983, 267-285. (1983) MR0706104
  10. M. W. Hirsch, Stability and convergence in strongly monotone dynamical sets, J. Reine Angew. Math. 383 (1988), 1-58. (1988) MR0921986
  11. H. Matano, Existence of nontrivial unstable sets for equilibriums of strongly orderpreserving systems, J. Fac. Sci. Univ. Tokyo 30 (1983), 645-673. (1983) MR0731522
  12. H. Matano, Correction to: "Existence of nontrivial unstable sets for equilibriums of strongly order-preserving systems", J. Fac. Sci. Univ. Tokyo 34 (1987), 853-855. (1987) Zbl0656.35009MR0927615
  13. H. Matano, Strong comparison principle in nonlinear parabolic equations, in "Nonlinear Parabolic Equations: Qualitative Properties of Solutions", L. Boccardo, A. Tesei (eds.), 148-155, Pitman, London 1987. (1987) Zbl0664.35048MR0901104
  14. J. Mierczyński, On a generic behaviour in strongly cooperative differential equations, Proceedings of the Third Colloquium on Qualitative Properties of Differential Equations, L. Hatvani (ed.), to appear. MR1062664
  15. J. Mierczyński P. Poláčik, Symmetry actions on strongly monotone dynamical systems, Math. Annalen 283 (1989), 1-11. (1989) MR0973801
  16. J. Palis W. de Melo, Geometric Theory of Dynamical Systems, Springer - Verlag, New York 1982. (1982) MR0669541
  17. P. Poláčik, Convergence in smooth strongly monotone flows defined by semilinear parabolic equations, J. Diff. Eqn. 79 (1989), 89-110. (1989) MR0997611
  18. P. Poláčik, Domains of attraction of equilibria and monotonicity properties of convergent trajectories in semilinear parabolic systems admitting strong comparison principle, J. Reine Angew. Math. 400 (1989), 32-56. (1989) MR1013724
  19. P. Poláčik, Generic properties of strongly monotone semiflows defined by ordinary and parabolic differential equations, Proceedings of the Third Colloquium on Qualitative Properties of Differential Equations, L. Hatvani (ed.), to appear. MR1062675
  20. H. L. Smith, Monotone semiflows generated by functional differential equations, J. Diff. Eqn. 66 (1987), 420-442. (1987) Zbl0612.34067MR0876806
  21. H. L. Smith, Systems of ordinary differential equations which generate an order preserving flow, A survey of results, SIAM Review 30 (1988), 87-114. (1988) Zbl0674.34012MR0931279
  22. H. L. Smith H. R. Thieme, Monotone semiflows in scalar non-quasimonotone functional differential equations, J. Math. Anal. Appl., to appear. MR1067429
  23. H. L. Smith H. R. Thieme, Remarks on monotone dynamical systems, preprint. 

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.