### 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→ - ∞, 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.

Lingua originale | English |
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pagine (da-a) | 221-251 |

Numero di pagine | 31 |

Rivista | Applied Mathematics and Optimization |

Volume | 81 |

Stato di pubblicazione | Published - 2020 |

### All Science Journal Classification (ASJC) codes

- Control and Optimization
- Applied Mathematics

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## Cita questo

Vetro, C., & Papageorgiou, N. S. (2020). (p, 2)-Equations with a Crossing Nonlinearity and Concave Terms.

*Applied Mathematics and Optimization*,*81*, 221-251.