Positive solutions for singular (p, 2)-equations

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


We consider a nonlinear nonparametric Dirichlet problem driven by the sum of a p-Laplacian and of a Laplacian (a (p, 2)-equation) and a reaction which involves a singular term and a \((p-1)\)-superlinear perturbation. Using variational tools and suitable truncation and comparison techniques, we show that the problem has two positive smooth solutions.


Singular term Superlinear perturbation Positive solution Nonlinear regularity Truncation Maximum principle Double phase problem 

Mathematics Subject Classification

35J20 35J75 35J92 



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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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