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Mathematische Annalen

, Volume 283, Issue 1, pp 1–11 | Cite as

Group actions on strongly monotone dynamical systems

  • Janusz Mierczyński
  • Peter Poláčik
Article

Keywords

Dynamical System Group Action Monotone Dynamical System 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. 1.
    Amann, H.: Fixed point equations and nonlinear eigenvalue problems in ordered Banach spaces. SIAM Rev.18, 620–709 (1976)Google Scholar
  2. 2.
    Amann, H.: Quasilinear evolution equations and parabolic systems. Trans. Am. Math. Soc.293, 191–227 (1986)Google Scholar
  3. 3.
    Amann, H.: Quasilinear parabolic systems under nonlinear boundary conditions. Arch. Rat. Mech. Anal.92, 153–192 (1986)Google Scholar
  4. 4.
    Amann, H.: Parabolic evolution equations and nonlinear boundary conditions. J. Differ. Equations72, 201–269 (1988)Google Scholar
  5. 5.
    Chernoff, P., Marsden, J.E.: On continuity and smoothness of group actions. Bull. Am. Math. Soc.76, 1044–1049 (1970)Google Scholar
  6. 6.
    Golubitsky, M., Schaeffer, D.: Singularities and groups in bifurcation theory. Applied Mathematical Sciences 51. Berlin Heidelberg New York: Springer 1986Google Scholar
  7. 7.
    Henry, D.: Geometric theory of semilinear parabolic equations. Lecture Notes Mathematics. Vol. 840. Berlin Heidelberg New York: Springer 1981Google Scholar
  8. 8.
    Hirsch, M.W.: Differential equations and convergence almost everywhere in strongly monotone flows. Contemp. Math.37, 267–282 (1983)Google Scholar
  9. 9.
    Hirsch, M.W.: The dynamical systems approach to differential equations. Bull. Am. Math. Soc., New Ser11, 1–64 (1984)Google Scholar
  10. 10.
    Hirsch, M.W.: Stability and convergence in strongly monotone dynamical systems. J. Reine Angew. Math.383, 1–53 (1988)Google Scholar
  11. 11.
    Lions, P.L.: Structure of the set of steady-state solutions of semilinear heat equations. J. Differ. Equations53, 362–386 (1984)Google Scholar
  12. 12.
    Martin, Jr., R.H.: A maximum principle for semilinear parabolic systems. Proc. Am. Math. Soc.74, 66–70 (1979)Google Scholar
  13. 13.
    Matano, H.: Existence of nontrivial unstable sets for equilibriums of strongly order-preserving systems. J. Fac. Sci., Univ. Tokyo, Sect. I A30, 645–673 (1984)Google Scholar
  14. 14.
    Matano, H.: Strongly order-preserving local semidynamical systems — theory and applications. In: Semigroups, theory and applications. Vol. I, Trieste 1984. (Pitman Research Notes Mathematics Series 141, pp. 178–185) Harlow: Longman 1986Google Scholar
  15. 15.
    Montgomery, D., Zippin, L.: Topological transformation groups. Interscience Tracts in Pure and Applied Mathematics. 1. New York: Interscience 1955Google Scholar
  16. 16.
    Mora, X.: Semilinear problems define semiflows onC k spaces. Trans. Am. Math. Soc.278, 21–55 (1983)Google Scholar
  17. 17.
    Poláčik, P.: Convergence in smooth strongly monotone flows defined by semilinear parabolic equations. J. Differ. Equations (to appear)Google Scholar
  18. 18.
    Sattinger, D.H.: Bifurcation and symmetry breaking in applied mathematics. Bull. Am. Math. Soc., New Ser.3, 779–819 (1980)Google Scholar
  19. 19.
    Triebel, H.: Interpolation theory, function spaces, differential operators. Berlin: Deutscher Verlag der Wissenschaften 1978Google Scholar
  20. 20.
    Vanderbauwhede, A.: Local bifurcation and symmetry. Research Notes Mathematics. Vol. 75. Boston: Pitman 1982Google Scholar

Copyright information

© Springer-Verlag 1989

Authors and Affiliations

  • Janusz Mierczyński
    • 1
  • Peter Poláčik
    • 2
  1. 1.Institute of MathematicsTechnical University of WroclawWroclawPoland
  2. 2.Institute of Applied MathematicsComenius UniversityBratislavaCzechoslovakia

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