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Positivity

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Singular Neumann (p, q)-equations

  • Nikolaos S. Papageorgiou
  • Calogero Vetro
  • Francesca VetroEmail author
Article
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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.

Keywords

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

Mathematics Subject Classification

35J92 35P30 
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Notes

Acknowledgements

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

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© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Department of MathematicsNational Technical UniversityAthensGreece
  2. 2.Department of Mathematics and Computer ScienceUniversity of PalermoPalermoItaly
  3. 3.Nonlinear Analysis Research GroupTon Duc Thang UniversityHo Chi Minh CityVietnam
  4. 4.Faculty of Mathematics and StatisticsTon Duc Thang UniversityHo Chi Minh CityVietnam

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