### Abstract

We consider semilinear elliptic problems in which the right-hand-side nonlinearity depends on a parameterλ > 0. Two multiplicity results are presented, guaranteeing the existence of at least three non-trivial solutions for this kind of problem, when the parameter belongs to an interval (0,*). Our approach is based on variational techniques, truncation methods and critical groups. The first result incorporates as a special case problems with concaveconvex nonlinearities, while the second one involves concave nonlinearities perturbed by an asymptotically linear nonlinearity at infinity.

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

Pages (from-to) | 171-180 |

Number of pages | 10 |

Journal | Proceedings of the Edinburgh Mathematical Society |

Volume | 52 |

Issue number | 1 |

DOIs | |

Publication status | Published - Feb 2009 |

### Fingerprint

### Keywords

- Critical groups
- Critical point
- Local minimizer
- Truncated functional

### ASJC Scopus subject areas

- Mathematics(all)

### Cite this

*Proceedings of the Edinburgh Mathematical Society*,

*52*(1), 171-180. https://doi.org/10.1017/S0013091507000665

**Multiplicity theorems for semilinear elliptic problems depending on a parameter.** / Kristály, A.; Papageorgiou, Nikolaos S.

Research output: Contribution to journal › Article

*Proceedings of the Edinburgh Mathematical Society*, vol. 52, no. 1, pp. 171-180. https://doi.org/10.1017/S0013091507000665

}

TY - JOUR

T1 - Multiplicity theorems for semilinear elliptic problems depending on a parameter

AU - Kristály, A.

AU - Papageorgiou, Nikolaos S.

PY - 2009/2

Y1 - 2009/2

N2 - We consider semilinear elliptic problems in which the right-hand-side nonlinearity depends on a parameterλ > 0. Two multiplicity results are presented, guaranteeing the existence of at least three non-trivial solutions for this kind of problem, when the parameter belongs to an interval (0,*). Our approach is based on variational techniques, truncation methods and critical groups. The first result incorporates as a special case problems with concaveconvex nonlinearities, while the second one involves concave nonlinearities perturbed by an asymptotically linear nonlinearity at infinity.

AB - We consider semilinear elliptic problems in which the right-hand-side nonlinearity depends on a parameterλ > 0. Two multiplicity results are presented, guaranteeing the existence of at least three non-trivial solutions for this kind of problem, when the parameter belongs to an interval (0,*). Our approach is based on variational techniques, truncation methods and critical groups. The first result incorporates as a special case problems with concaveconvex nonlinearities, while the second one involves concave nonlinearities perturbed by an asymptotically linear nonlinearity at infinity.

KW - Critical groups

KW - Critical point

KW - Local minimizer

KW - Truncated functional

UR - http://www.scopus.com/inward/record.url?scp=68349139222&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=68349139222&partnerID=8YFLogxK

U2 - 10.1017/S0013091507000665

DO - 10.1017/S0013091507000665

M3 - Article

VL - 52

SP - 171

EP - 180

JO - Proceedings of the Edinburgh Mathematical Society

JF - Proceedings of the Edinburgh Mathematical Society

SN - 0013-0915

IS - 1

ER -