On the Variational Eigenvalues Which Are Not of Ljusternik-Schnirelmann Type

Abstract EN

We discuss nonlinear homogeneous eigenvalue problems and the variational characterization of their eigenvalues.

We focus on the Ljusternik-Schnirelmann method, present one possible alternative to this method and compare it with the Courant-Fischer minimax principle in the linear case.

At the end we present a special nonlinear eigenvalue problem possessing an eigenvalue which allows the variational characterization but is not of Ljusternik-Schnirelmann type.