Lusternik-Schnirelman category theory on closed subsets of Banach manifolds
The first part of the paper contains a result on the existence of pseudogradient vector fields for a \(C^ 2\)-real valued function on a closed subset of a \(C^ 2\)-Banach manifold. The author uses this result to prove an extension of Palais' existence theorem for the minimization problem. In the second part the author extends Lusternik-Schnirelman category theory on Banach manifolds to closed subsets of them, enunciating several results related with this. He finishes the paper studying the geodesic problem.
Lusternik- Schnirelman category theory on Banach manifolds
scientific article; zbMATH DE number 4166099