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

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Abstract

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.

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Acknowledgments

The authors have been supported by the “Gruppo Nazionale per l’Analisi Matematica, la Probabilità e le loro Applicazioni (GNAMPA)” of the Istituto Nazionale di Alta Matematica (INdAM).

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Authors and Affiliations

  1. Dipartimento di Matematica, Università di Roma “Tor Vergata”, Via della Ricerca Scientifica n. 1, 00133, Rome, Italy

    Riccardo Molle

  2. Dipartimento di Matematica “E. De Giorgi”, Università di Lecce, P.O. Box 193, 73100, Lecce, Italy

    Donato Passaseo

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  1. Riccardo Molle
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  2. Donato Passaseo
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Correspondence to Riccardo Molle.

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Communicated by P. Rabinowitz.

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Molle, R., Passaseo, D. Variational properties of the first curve of the Fučík spectrum for elliptic operators. Calc. Var. 54, 3735–3752 (2015). https://doi.org/10.1007/s00526-015-0920-4

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