A relation between critical values and eigenvalues in nonliner minimax problems

Abstract

The paper establishes a relation between constrained minimax values of a functional g on a Hilbert space and related eigenvalues. If g is Frechet differentiable and weakly continuous, in presence of a saddle point geometry the minimax value σ(t) of g over corresponds to a set of eigenfunctions satisfying Moreover,γ has left and right hand derivatives and each of the is an eigenvalue. This abstract statement is written in mind of applications to existence of multiple nodal solutions for quasilinear elliptic equations.

Keywords:

• Variational Problems
• eigenvalues
• minimax