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

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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

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  7. M. W. Hirsch, Systems of differential equations that are competitive or cooperative. III: Competing species, Nonlinearity 1 (1988), 51-71. (1988) Zbl0658.34024MR0928948
  8. M. W. Hirsch, The dynamical systems approach to differential equations, Bull. AMS 11 (1984), 1-64. (1984) Zbl0541.34026MR0741723
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  10. M. W. Hirsch, Stability and convergence in strongly monotone dynamical sets, J. Reine Angew. Math. 383 (1988), 1-58. (1988) Zbl0624.58017MR0921986
  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. Zbl0705.34027MR1062664
  15. J. Mierczyński P. Poláčik, Symmetry actions on strongly monotone dynamical systems, Math. Annalen 283 (1989), 1-11. (1989) Zbl0642.58031MR0973801
  16. J. Palis W. de Melo, Geometric Theory of Dynamical Systems, Springer - Verlag, New York 1982. (1982) Zbl0491.58001MR0669541
  17. P. Poláčik, Convergence in smooth strongly monotone flows defined by semilinear parabolic equations, J. Diff. Eqn. 79 (1989), 89-110. (1989) Zbl0684.34064MR0997611
  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) Zbl0667.35036MR1013724
  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. Zbl0714.58043MR1062675
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  23. H. L. Smith H. R. Thieme, Remarks on monotone dynamical systems, preprint. 

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