(p, 2)-Equations with a Crossing Nonlinearity and Concave Terms

  • Nikolaos S. Papageorgiou
  • Calogero Vetro
  • Francesca Vetro
Article
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Abstract

We consider a parametric Dirichlet problem driven by the sum of a p-Laplacian (\(p>2\)) and a Laplacian (a (p, 2)-equation). The reaction consists of an asymmetric \((p-1)\)-linear term which is resonant as \(x \rightarrow - \infty \), plus a concave term. However, in this case the concave term enters with a negative sign. Using variational tools together with suitable truncation techniques and Morse theory (critical groups), we show that when the parameter is small the problem has at least three nontrivial smooth solutions.

Keywords

p-Laplacian Concave term Crossing nonlinearity Nonlinear regularity Nonlinear maximum principle Critical groups Multiple smooth solutions 

Mathematics Subject Classification

35J20 35J60 58E05 

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Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  • Nikolaos S. Papageorgiou
    • 1
  • Calogero Vetro
    • 2
  • Francesca Vetro
    • 3
  1. 1.Department of MathematicsNational Technical UniversityAthensGreece
  2. 2.Department of Mathematics and Computer ScienceUniversity of PalermoPalermoItaly
  3. 3.Department of Energy, Information Engineering and Mathematical ModelsUniversity of PalermoPalermoItaly

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