Resumen de On variational eigenvalues of the p-Laplacian which are not of Ljusternik�Schnirelmann type

Pavel Drábek, Peter Takác

• In this paper we demonstrate the fact that the famous Ljusternik�Schnirelmann characterization of some eigenvalues of nonlinear elliptic problems (by a minimax formula) has a global variational character. Indeed, we show that, for some homogeneous quasilinear elliptic eigenvalue problems, there are variational eigenvalues other than those of the Ljusternik�Schnirelmann type. In contrast, these eigenvalues have a local variational character. Such a phenomenon does not occur in typical linear elliptic eigenvalue problems, owing to the Courant�Fischer theorem which is the linear analogue and predecessor of the Ljusternik�Schnirelmann theory.