Lusternik-Schnirelmann theory for fixed points of maps
KeywordsFixed point theory, Lusternik-Schnirelman theory, Palais-Smale condition
AbstractWe use the ideas of Lusternik-Schnirelmann theory to describe the set of fixed points of certain homotopy equivalences of a general space. In fact, we extend Lusternik-Schnirelmann theory to pairs $(\varphi, f)$, where $\varphi$ is a homotopy equivalence of a topological space $X$ and where $f \colon X \rightarrow \mathbb R$ is a continuous function satisfying $f(\varphi(x)) < f(x)$ unless $\varphi (x) = x$; in addition, the pair $(\varphi, f)$ is supposed to satisfy a discrete analogue of the Palais-Smale condition. In order to estimate the number of fixed points of $\varphi$ in a subset of $X$, we consider different relative categories. Moreover, the theory is carried out in an equivariant setting.
How to Cite
RUDYAK, Yuli B. & SCHLENK, Felix. Lusternik-Schnirelmann theory for fixed points of maps. Topological Methods in Nonlinear Analysis [online]. 1 March 2003, T. 21, nr 1, s. 171–194. [accessed 25.3.2023].
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