Geodesic
Existence of unstable sets for invariant sets in compact semiflows. Applications in order-preserving semiflows
Commentationes Mathematicae Universitatis Carolinae, Tome 31 (1990) no. 2, pp. 263-276 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

Voir la notice de l'article

Classification : 34C30, 34C35, 35B40, 37-99, 37C10, 58F25 
@article{CMUC_1990_31_2_a8,
     author = {Pol\'a\v{c}ik, Peter},
     title = {Existence of unstable sets for invariant sets in compact semiflows. {Applications} in order-preserving semiflows},
     journal = {Commentationes Mathematicae Universitatis Carolinae},
     pages = {263--276},
     year = {1990},
     volume = {31},
     number = {2},
     mrnumber = {1077897},
     zbl = {0724.58054},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/CMUC_1990_31_2_a8/}
}
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
SP  - 263
EP  - 276
VL  - 31
IS  - 2
UR  - http://geodesic.mathdoc.fr/item/CMUC_1990_31_2_a8/
LA  - en
ID  - CMUC_1990_31_2_a8
ER  - 
%0 Journal Article
%A Poláčik, Peter
%T Existence of unstable sets for invariant sets in compact semiflows. Applications in order-preserving semiflows
%J Commentationes Mathematicae Universitatis Carolinae
%D 1990
%P 263-276
%V 31
%N 2
%U http://geodesic.mathdoc.fr/item/CMUC_1990_31_2_a8/
%G en
%F CMUC_1990_31_2_a8
Poláčik, Peter. Existence of unstable sets for invariant sets in compact semiflows. Applications in order-preserving semiflows. Commentationes Mathematicae Universitatis Carolinae, Tome 31 (1990) no. 2, pp. 263-276. http://geodesic.mathdoc.fr/item/CMUC_1990_31_2_a8/

[AHM] N. D. Alikakos P. Hess H. Matano: Discrete order preserving semigroups and stability for periodic parabolic differential equations. preprint. | MR

[H1] J. K. Hale: Theory of Functional Differential Equations. Springer-Verlag, New York 1977. | MR | Zbl

[H2] J. K. Hale: Asymptotic Behaviour of Dissipative Systems. AMS Publications, Providence 1988. | MR

[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

[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

[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. | MR | Zbl

[Hi3] M. W. Hirsch: Systems of differential equations that are competitive or cooperative. III: Competing species. Nonlinearity 1 (1988), 51-71. | MR

[Hi4] M. W. Hirsch: The dynamical systems approach to differential equations. Bull. AMS 11 (1984), 1-64. | MR | Zbl

[Hi5] M. W. Hirsch: Differential equations and convergence almost everywhere in strongly monotone flows. Contemporary Math. 17, Providence 1983, 267-285. | MR

[Hi6] M. W. Hirsch: Stability and convergence in strongly monotone dynamical sets. J. Reine Angew. Math. 383 (1988), 1-58. | MR

[M1] H. Matano: Existence of nontrivial unstable sets for equilibriums of strongly orderpreserving systems. J. Fac. Sci. Univ. Tokyo 30 (1983), 645-673. | MR

[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. | MR | Zbl

[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. | MR | Zbl

[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

[MP] J. Mierczyński P. Poláčik: Symmetry actions on strongly monotone dynamical systems. Math. Annalen 283 (1989), 1-11. | MR

[PM] J. Palis W. de Melo: Geometric Theory of Dynamical Systems. Springer - Verlag, New York 1982. | MR

[P1] P. Poláčik: Convergence in smooth strongly monotone flows defined by semilinear parabolic equations. J. Diff. Eqn. 79 (1989), 89-110. | MR

[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

[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

[S1] H. L. Smith: Monotone semiflows generated by functional differential equations. J. Diff. Eqn. 66 (1987), 420-442. | MR | Zbl

[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. | MR | Zbl

[ST1] H. L. Smith H. R. Thieme: Monotone semiflows in scalar non-quasimonotone functional differential equations. J. Math. Anal. Appl., to appear. | MR

[ST2] H. L. Smith H. R. Thieme: Remarks on monotone dynamical systems. preprint.