Variational properties of the first curve of the Fučík spectrum for elliptic operators

In this paper we present a new variational characteriztion of the first nontrival curve of the Fučík spectrum for elliptic operators with Dirichlet 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 Molle and Passaseo, C R Math Acad Sci Paris 351:681–685, 2013; Ann I H Poincare—AN, 2014): 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.