### Abstract

We consider singularly perturbed nonlinear Schrödinger equations (Formula Presented) where (Formula Presented) and f is a nonlinear term which satisfies the so-called Berestycki–Lions conditions. We assume that there exists a bounded domain (Formula Presented) such that (Formula Presented) and we set (Formula Presented). For (Formula Presented) small we prove the existence of at least (Formula Presented) solutions to (0.1) concentrating, as (Formula Presented) around K. We remark that, under our assumptions of f, the search of solutions to (0.1) cannot be reduced to the study of the critical points of a functional restricted to a Nehari manifold.

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

Pages (from-to) | 413-439 |

Number of pages | 27 |

Journal | Calculus of Variations and Partial Differential Equations |

Volume | 53 |

Issue number | 1-2 |

DOIs | |

Publication status | Published - 2015 |

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### ASJC Scopus subject areas

- Analysis
- Applied Mathematics

### Cite this

*Calculus of Variations and Partial Differential Equations*,

*53*(1-2), 413-439. https://doi.org/10.1007/s00526-014-0754-5

**Multiplicity of positive solutions of nonlinear Schrödinger equations concentrating at a potential well.** / Cingolani, Silvia; Jeanjean, Louis; Tanaka, Kazunaga.

Research output: Contribution to journal › Article

*Calculus of Variations and Partial Differential Equations*, vol. 53, no. 1-2, pp. 413-439. https://doi.org/10.1007/s00526-014-0754-5

}

TY - JOUR

T1 - Multiplicity of positive solutions of nonlinear Schrödinger equations concentrating at a potential well

AU - Cingolani, Silvia

AU - Jeanjean, Louis

AU - Tanaka, Kazunaga

PY - 2015

Y1 - 2015

N2 - We consider singularly perturbed nonlinear Schrödinger equations (Formula Presented) where (Formula Presented) and f is a nonlinear term which satisfies the so-called Berestycki–Lions conditions. We assume that there exists a bounded domain (Formula Presented) such that (Formula Presented) and we set (Formula Presented). For (Formula Presented) small we prove the existence of at least (Formula Presented) solutions to (0.1) concentrating, as (Formula Presented) around K. We remark that, under our assumptions of f, the search of solutions to (0.1) cannot be reduced to the study of the critical points of a functional restricted to a Nehari manifold.

AB - We consider singularly perturbed nonlinear Schrödinger equations (Formula Presented) where (Formula Presented) and f is a nonlinear term which satisfies the so-called Berestycki–Lions conditions. We assume that there exists a bounded domain (Formula Presented) such that (Formula Presented) and we set (Formula Presented). For (Formula Presented) small we prove the existence of at least (Formula Presented) solutions to (0.1) concentrating, as (Formula Presented) around K. We remark that, under our assumptions of f, the search of solutions to (0.1) cannot be reduced to the study of the critical points of a functional restricted to a Nehari manifold.

UR - http://www.scopus.com/inward/record.url?scp=84939891674&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84939891674&partnerID=8YFLogxK

U2 - 10.1007/s00526-014-0754-5

DO - 10.1007/s00526-014-0754-5

M3 - Article

VL - 53

SP - 413

EP - 439

JO - Calculus of Variations and Partial Differential Equations

JF - Calculus of Variations and Partial Differential Equations

SN - 0944-2669

IS - 1-2

ER -