Geometric Variational Problems and Lusternik-Schnirelman Theory

In this book, we showed the Lusternik-Schnirelman theory for the existence and multiplicity of solutions to nonlinear eigenvalue problems, by using the topological concepts of Krasnoselskii's Genus and Lusternik-Schnirelman Category. The book is motivated by a work of Amann and some ideas of geometric analysis pertaining to the Mountain Pass Lemma. The key goal is to show the technique of solving analytical problems via an understanding of the geometric properties of the functionals associated with them. This simple idea of viewing the interplay between Analysis and Geometry is a very influential and classical technique of Mathematics