A relative variant of the Morse theory
The standard Morse theory has been established for \(C^{1,1}\)-functionals defined on a Hilbert manifold. In the paper under review the smoothness of the functionals is reduced by one, hence the author is concerned with Morse-type results for Lipschitz functionals. The main result establishes the invariance of topological characteristics of functionals under uniform deformations. The developed results can be used for estimating the number of solutions of variational inequalities and for the study of conditions for extrema of functionals depending on a parameter.
scientific article; zbMATH DE number 6152658