The cohomological span of LS-Conley index

Jakub Maksymiuk

doi:10.1016/j.jde.2015.07.002

The cohomological span of LS-Conley index

Abstract

In this paper we introduce a new homotopy invariant – the cohomological span of LS-Conley index. We prove the theorems on the existence of critical points for a class of strongly indefinite functionals with the gradient of the form Lx+K(x), where L is bounded linear and K is completely continuous. We give examples of Hamiltonian systems for which our methods give better results than the Morse inequalities. We also give a formula for the LS-index of an isolated critical point, which is an extension of the classical Dancer theorem for the case of LS-index.

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DOI:: Digital Object Identifier (open in new tab) 10.1016/j.jde.2015.07.002
License: Copyright (2015 Elsevier Inc.)

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Category:: Articles
Type:: artykuł w czasopiśmie wyróżnionym w JCR
Published in:: JOURNAL OF DIFFERENTIAL EQUATIONS no. 259, edition 11, pages 5640 - 5666,
ISSN: 0022-0396
Language:: English
Publication year:: 2015
Bibliographic description:: Maksymiuk J.: The cohomological span of LS-Conley index// JOURNAL OF DIFFERENTIAL EQUATIONS. -Vol. 259, iss. 11 (2015), s.5640-5666
DOI:: Digital Object Identifier (open in new tab) 10.1016/j.jde.2015.07.002
Verified by:: Gdańsk University of Technology