Singular Neumann (pq)-equations

Abstract

We consider a nonlinear parametric Neumann problem driven by the sum of a p-Laplacian and of a q-Laplacian and exhibiting in the reaction the competing effects of a singular term and of a resonant term. Using variational methods together with suitable truncation and comparison techniques, we show that for small values of the parameter the problem has at least two positive smooth solutions.

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Acknowledgements

The authors wish to thank a knowledgeable referee for his/her corrections and remarks.

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Correspondence to Francesca Vetro.

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Papageorgiou, N.S., Vetro, C. & Vetro, F. Singular Neumann (pq)-equations. Positivity 24, 1017–1040 (2020). https://doi.org/10.1007/s11117-019-00717-w

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Keywords

  • Singular term
  • Resonant nonlinearity
  • Nonlinear regularity
  • Truncation and comparison
  • Nonlinear strong maximum principle
  • (p, q)-equation

Mathematics Subject Classification

  • 35J92
  • 35P30