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

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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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

Mathematics Subject Classification

  • 35J20
  • 35J60
  • 58E05