Conley type index and Hamiltonian inclusions

Zdzisław Dzedzej

Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica (2010)

  • Volume: 49, Issue: 1, page 33-47
  • ISSN: 0231-9721

Abstract

top
This paper is based mainly on the joint paper with W. Kryszewski [Dzedzej, Z., Kryszewski, W.: Conley type index applied to Hamiltonian inclusions. J. Math. Anal. Appl. 347 (2008), 96–112.], where cohomological Conley type index for multivalued flows has been applied to prove the existence of nontrivial periodic solutions for asymptotically linear Hamiltonian inclusions. Some proofs and additional remarks concerning definition of the index and special cases are given.

How to cite

top

Dzedzej, Zdzisław. "Conley type index and Hamiltonian inclusions." Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica 49.1 (2010): 33-47. <http://eudml.org/doc/116475>.

@article{Dzedzej2010,
abstract = {This paper is based mainly on the joint paper with W. Kryszewski [Dzedzej, Z., Kryszewski, W.: Conley type index applied to Hamiltonian inclusions. J. Math. Anal. Appl. 347 (2008), 96–112.], where cohomological Conley type index for multivalued flows has been applied to prove the existence of nontrivial periodic solutions for asymptotically linear Hamiltonian inclusions. Some proofs and additional remarks concerning definition of the index and special cases are given.},
author = {Dzedzej, Zdzisław},
journal = {Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica},
keywords = {Conley index; multivalued dynamical system; Hamiltonian inclusion; Conley index; multivalued dynamical system; Hamiltonian inclusion},
language = {eng},
number = {1},
pages = {33-47},
publisher = {Palacký University Olomouc},
title = {Conley type index and Hamiltonian inclusions},
url = {http://eudml.org/doc/116475},
volume = {49},
year = {2010},
}

TY - JOUR
AU - Dzedzej, Zdzisław
TI - Conley type index and Hamiltonian inclusions
JO - Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica
PY - 2010
PB - Palacký University Olomouc
VL - 49
IS - 1
SP - 33
EP - 47
AB - This paper is based mainly on the joint paper with W. Kryszewski [Dzedzej, Z., Kryszewski, W.: Conley type index applied to Hamiltonian inclusions. J. Math. Anal. Appl. 347 (2008), 96–112.], where cohomological Conley type index for multivalued flows has been applied to prove the existence of nontrivial periodic solutions for asymptotically linear Hamiltonian inclusions. Some proofs and additional remarks concerning definition of the index and special cases are given.
LA - eng
KW - Conley index; multivalued dynamical system; Hamiltonian inclusion; Conley index; multivalued dynamical system; Hamiltonian inclusion
UR - http://eudml.org/doc/116475
ER -

References

top
  1. Amann, H., Zehnder, E., 10.1007/BF01298187, Manuscripta Math. 32 (1980), 149–189. (1980) Zbl0443.70019MR0592715DOI10.1007/BF01298187
  2. Bobylev, N. A., Bulatov, A. V., Kuznetsov, Yu. O., An approximation scheme for defining the Conley index of isolated critical points, Diff. Equ. 40 (2004), 1539–1544. (2004) Zbl1084.37015MR2200861
  3. Chang, K. C., Liu, J. Q., Liu, M. J., 10.1016/S0294-1449(97)80150-3, Ann. Inst. Henri Poincare 14 (1997), 103–117. (1997) Zbl0881.34061MR1437190DOI10.1016/S0294-1449(97)80150-3
  4. Clarke, F. H., 10.1016/0022-0396(81)90007-3, J. Diff. Eq. 40 (1981), 1–6. (1981) Zbl0461.34030MR0614215DOI10.1016/0022-0396(81)90007-3
  5. Clarke, F. H., Optimization and Nonsmooth Analysis, Wiley, New York, 1983. (1983) Zbl0582.49001MR0709590
  6. Conley, C., Isolated Invariant Sets and the Morse Index, CBMS 38 Amer. Math. Society, Providence, Rhode Island, 1978. (1978) Zbl0397.34056MR0511133
  7. Dzedzej, Z., On the Conley index in Hilbert spaces – a multivalued case, Banach Center Publ. 77 Warszawa, 2007, 61–68. (2007) Zbl1114.37013MR2338575
  8. Dzedzej, Z., Gabor, G., On homotopy Conley index for multivalued flows in Hilbert spaces, to appear. 
  9. Dzedzej, Z., Kryszewski, W., 10.1016/j.jmaa.2008.05.081, J. Math. Anal. Appl. 347 (2008), 96–112. (2008) Zbl1149.37008MR2433828DOI10.1016/j.jmaa.2008.05.081
  10. Emelyanov, S. V., Korovin, S. K., Bobylev, N. A., Bulatov, A. V., Homotopy of Extremal Problems, W. de Gruyter, Berlin, 2007. (2007) Zbl1141.49001MR2352609
  11. Fei, G. H., 10.1006/jdeq.1995.1124, J. Differential Equations 121 (1995), 121–133. (1995) Zbl0831.34046MR1348538DOI10.1006/jdeq.1995.1124
  12. Gabor, G., 10.1007/s11228-004-4109-9, Set-valued Analysis 13 (2005), 125–149. (2005) Zbl1096.54016MR2148132DOI10.1007/s11228-004-4109-9
  13. Gȩba, K., Izydorek, M., Pruszko, A., The Conley index in Hilbert spaces and its applications, Studia Math. 134 (1999), 217–233. (1999) MR1685454
  14. Górniewicz, L., Topological Fixed Point Theory of Multivalued Mappings, Kluwer, Dordrecht–Boston–London, 1999. (1999) 
  15. Han, Z. Q., 10.1016/j.jmaa.2006.07.047, J. Math. Anal. Appl. 330 (2007), 259–275. (2007) Zbl1115.37056MR2302921DOI10.1016/j.jmaa.2006.07.047
  16. Izydorek, M., 10.1006/jdeq.2000.3818, J. Differential Equations 170 (2001), 22–50. (2001) MR1813098DOI10.1006/jdeq.2000.3818
  17. Izydorek, M., Rybakowski, K., 10.4064/fm171-1-2, Fund. Math. 171 (2002), 31–52. (2002) MR1879882DOI10.4064/fm171-1-2
  18. Kryszewski, W., Szulkin, A., 10.1090/S0002-9947-97-01963-6, Trans. Amer. Math. Soc. 349 (1997), 3181–3234. (1997) Zbl0892.58015MR1422612DOI10.1090/S0002-9947-97-01963-6
  19. Kunze, M., Küpper, T., Li, Y., On Conley index theory for non-smooth dynamical systems, Differential Integral Equations 13 (2000), 479–502. (2000) MR1750037
  20. Mrozek, M., 10.1016/0022-0396(90)90125-9, J. Differential Equations 84 (1990), 15–51. (1990) MR1042657DOI10.1016/0022-0396(90)90125-9
  21. Rybakowski, K., The Homotopy Index and Partial Differential Equations, Springer, Berlin, 1987. (1987) Zbl0628.58006MR0910097
  22. Szulkin, A., 10.1007/BF02570842, Math. Z. 209 (1992), 375–418. (1992) Zbl0735.58012MR1152264DOI10.1007/BF02570842
  23. Szulkin, A., Zhou, W., 10.1006/jdeq.2000.3942, J. Differential Equations 174 (2001), 369–391. (2001) MR1846740DOI10.1006/jdeq.2000.3942

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.