On the first curve of the Fučík spectrum for elliptic operators

Abstract

In this Note we present a new variational characterization of the first nontrivial curve of the Fučík spectrum for elliptic operators with Dirichlet or Neumann boundary conditions. Moreover, we describe the asymptotic behaviour and some properties of this curve and of the corresponding eigenfunctions. In particular, this new characterization allows us to compare the first curve of the Fučík spectrum with the infinitely many curves we obtained in previous works (see [8, 9]): for example, we show that these curves are all asymptotic to the same lines as the first curve, but they are all distinct from such a curve.