Lusternik-Schnirelmann theory for fixed points of maps
Keywords
Fixed point theory, Lusternik-Schnirelman theory, Palais-Smale conditionAbstract
We 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.Downloads
Published
2003-03-01
How to Cite
1.
RUDYAK, Yuli B. and SCHLENK, Felix. Lusternik-Schnirelmann theory for fixed points of maps. Topological Methods in Nonlinear Analysis. Online. 1 March 2003. Vol. 21, no. 1, pp. 171 - 194. [Accessed 19 September 2024].
Issue
Section
Articles
Stats
Number of views and downloads: 0
Number of citations: 0