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On resonant Neumann problems

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Abstract

We consider semilinear Neumann problems at resonance and prove existence and multiplicity theorems. The existence theorems allow resonance with respect to any eigenvalue of the negative Neumann Laplacian. The multiplicity theorems concern problems resonant at 0 (the principal eigenvalue) or at the first nonzero eigenvalue. Our approach uses tools from critical point theory and from Morse theory.

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Authors and Affiliations

  1. Département de Mathématiques, Université de Perpignan, 66860, Perpignan, France

    D. Motreanu

  2. Department of Mathematics, Ben Gurion University of the Negev, 84105, Be’er Sheva, Israel

    V. V. Motreanu

  3. Department of Mathematics, National Technical University, 15780, Athens, Greece

    N. S. Papageorgiou

Authors
  1. D. Motreanu
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  2. V. V. Motreanu
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  3. N. S. Papageorgiou
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Correspondence to D. Motreanu.

Additional information

V. V. Motreanu is grateful to the Center for Advanced Studies in Mathematics of the Ben-Gurion University of the Negev for partial support.

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Motreanu, D., Motreanu, V.V. & Papageorgiou, N.S. On resonant Neumann problems. Math. Ann. 354, 1117–1145 (2012). https://doi.org/10.1007/s00208-011-0763-z

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  • DOI: https://doi.org/10.1007/s00208-011-0763-z

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