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Pairs of solutions for Robin problems with an indefinite and unbounded potential, resonant at zero and infinity

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Abstract

We consider a semilinear Robin problem driven by the Laplacian plus an indefinite and unbounded potential and a Caratheodory reaction term which is resonant both at zero and \(\pm \infty \). Using the Lyapunov–Schmidt reduction method and critical groups (Morse theory), we show that the problem has at least two nontrivial smooth solutions.

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Authors and Affiliations

  1. Department of Mathematics, National Technical University, Zografou Campus, 15780, Athens, Greece

    Nikolaos S. Papageorgiou

  2. Department of Mathematics and Computer Science, University of Palermo, Via Archirafi 34, 90123, Palermo, Italy

    Calogero Vetro

  3. Department of Energy, Information Engineering and Mathematical Models (DEIM), University of Palermo, Viale delle Scienze ed. 8, 90128, Palermo, Italy

    Francesca Vetro

Authors
  1. Nikolaos S. Papageorgiou
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  2. Calogero Vetro
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  3. Francesca Vetro
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Correspondence to Nikolaos S. Papageorgiou.

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Papageorgiou, N.S., Vetro, C. & Vetro, F. Pairs of solutions for Robin problems with an indefinite and unbounded potential, resonant at zero and infinity. manuscripta math. 158, 487–503 (2019). https://doi.org/10.1007/s00229-018-1044-x

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  • DOI: https://doi.org/10.1007/s00229-018-1044-x

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