### 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.

Original language | English |
---|---|

Pages (from-to) | 221-251 |

Number of pages | 31 |

Journal | Applied Mathematics and Optimization |

Volume | 81 |

Publication status | Published - 2020 |

### All Science Journal Classification (ASJC) codes

- Control and Optimization
- Applied Mathematics

## Fingerprint Dive into the research topics of '(p, 2)-Equations with a Crossing Nonlinearity and Concave Terms'. Together they form a unique fingerprint.

## Cite this

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

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