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Conley type index applied to Hamiltonian inclusions. (English) Zbl 1149.37008

The authors introduce and develop the theory of a cohomological Conley type index as an infinite-dimensional counterpart of the Mrozek index by use of methods by K. Gȩba, M. Izydorek and A. Pruszko [Stud. Math. 134, No. 3, 217–233 (1999; Zbl 0927.58004)] and the author [in: J. Jachymski (ed.) et al., Fixed point theory and its applications, Proceedings of the international conference, Bedlewo, Poland, August 1–5, 2005, Warsaw: Polish Academy of Sciences, Institute of Mathematics, Banach Center Publications 77, 61–68 (2007; Zbl 1114.37013)], and apply it to study the existence of periodic orbits of Hamiltonian systems involving nonsmooth Hamiltonian (asymptotically linear Hamiltonian inclusions).

MSC:

37B30 Index theory for dynamical systems, Morse-Conley indices
34A60 Ordinary differential inclusions
37J45 Periodic, homoclinic and heteroclinic orbits; variational methods, degree-theoretic methods (MSC2010)
47J05 Equations involving nonlinear operators (general)
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