| Title:
|
Existence of unstable sets for invariant sets in compact semiflows. Applications in order-preserving semiflows (English) |
| Author:
|
Poláčik, Peter |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
31 |
| Issue:
|
2 |
| Year:
|
1990 |
| Pages:
|
263-276 |
| . |
| Category:
|
math |
| . |
| MSC:
|
34C30 |
| MSC:
|
34C35 |
| MSC:
|
35B40 |
| MSC:
|
37-99 |
| MSC:
|
37C10 |
| MSC:
|
58F25 |
| idZBL:
|
Zbl 0724.58054 |
| idMR:
|
MR1077897 |
| . |
| Date available:
|
2008-06-05T21:43:45Z |
| Last updated:
|
2012-04-28 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/106856 |
| . |
| Reference:
|
[AHM] N. D. Alikakos P. Hess H. Matano: Discrete order preserving semigroups and stability for periodic parabolic differential equations.preprint. MR 1027972 |
| Reference:
|
[H1] J. K. Hale: Theory of Functional Differential Equations.Springer-Verlag, New York 1977. Zbl 0352.34001, MR 0508721 |
| Reference:
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[H2] J. K. Hale: Asymptotic Behaviour of Dissipative Systems.AMS Publications, Providence 1988. MR 0941371 |
| Reference:
|
[He] 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. MR 1009399 |
| Reference:
|
[Hi1] M. W. Hirsch: Systems of differential equations that are competitive or cooperative. I: Limit sets.SIAM J. Math. Anal. 13 (1982), 167-179. MR 0647119 |
| Reference:
|
[Hi2] M. W. Hirsch: Systems of differential equations that are competitive or cooperative. II: Convergence almost everywhere.SIAM J. Math. Anal. 16 (1985), 423-439. Zbl 0658.34023, MR 0783970 |
| Reference:
|
[Hi3] M. W. Hirsch: Systems of differential equations that are competitive or cooperative. III: Competing species.Nonlinearity 1 (1988), 51-71. MR 0928948 |
| Reference:
|
[Hi4] M. W. Hirsch: The dynamical systems approach to differential equations.Bull. AMS 11 (1984), 1-64. Zbl 0541.34026, MR 0741723 |
| Reference:
|
[Hi5] M. W. Hirsch: Differential equations and convergence almost everywhere in strongly monotone flows.Contemporary Math. 17, Providence 1983, 267-285. MR 0706104 |
| Reference:
|
[Hi6] M. W. Hirsch: Stability and convergence in strongly monotone dynamical sets.J. Reine Angew. Math. 383 (1988), 1-58. MR 0921986 |
| Reference:
|
[M1] H. Matano: Existence of nontrivial unstable sets for equilibriums of strongly orderpreserving systems.J. Fac. Sci. Univ. Tokyo 30 (1983), 645-673. MR 0731522 |
| Reference:
|
[M2] 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. Zbl 0656.35009, MR 0927615 |
| Reference:
|
[M3] 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. Zbl 0664.35048, MR 0901104 |
| Reference:
|
[Mi] 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. MR 1062664 |
| Reference:
|
[MP] J. Mierczyński P. Poláčik: Symmetry actions on strongly monotone dynamical systems.Math. Annalen 283 (1989), 1-11. MR 0973801 |
| Reference:
|
[PM] J. Palis W. de Melo: Geometric Theory of Dynamical Systems.Springer - Verlag, New York 1982. MR 0669541 |
| Reference:
|
[P1] P. Poláčik: Convergence in smooth strongly monotone flows defined by semilinear parabolic equations.J. Diff. Eqn. 79 (1989), 89-110. MR 0997611 |
| Reference:
|
[P2] 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. MR 1013724 |
| Reference:
|
[P3] 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. MR 1062675 |
| Reference:
|
[S1] H. L. Smith: Monotone semiflows generated by functional differential equations.J. Diff. Eqn. 66 (1987), 420-442. Zbl 0612.34067, MR 0876806 |
| Reference:
|
[S2] H. L. Smith: Systems of ordinary differential equations which generate an order preserving flow, A survey of results.SIAM Review 30 (1988), 87-114. Zbl 0674.34012, MR 0931279 |
| Reference:
|
[ST1] H. L. Smith H. R. Thieme: Monotone semiflows in scalar non-quasimonotone functional differential equations.J. Math. Anal. Appl., to appear. MR 1067429 |
| Reference:
|
[ST2] H. L. Smith H. R. Thieme: Remarks on monotone dynamical systems.preprint. |
| . |
