The cohomological span of -Conley index

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• 作者：Jakub Maksymiuk ^{jmaksymiuk@mif.pg.gda.pl" class="auth_mail" title="E-mail the corresponding author}
• 关键词：37B30 ; 58E05
• 刊名：Journal of Differential Equations
• 出版年：2015
• 出版时间：5 December 2015
• 年：2015
• 卷：259
• 期：11
• 页码：5640-5666
• 全文大小：392 K

文摘

In this paper we introduce a new homotopy invariant – the cohomological span of LS$\mathcal{LS}$-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)$Lx+K(x)$, 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$\mathcal{LS}$-index of an isolated critical point, which is an extension of the classical Dancer theorem for the case of LS$\mathcal{LS}$-index.