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

Calogero Vetro, Nikolaos S. Papageorgiou

Research output: Contribution to journalArticlepeer-review

6 Citations (Scopus)


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→ - ∞, 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.
Original languageEnglish
Pages (from-to)221-251
Number of pages31
JournalApplied Mathematics and Optimization
Publication statusPublished - 2020

All Science Journal Classification (ASJC) codes

  • Control and Optimization
  • Applied Mathematics


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