Title | PARAMETRIC p-LAPLACIAN EQUATIONS WITH SUPERLINEAR REACTIONS |

Publication Type | Journal Article |

Year of Publication | 2015 |

Authors | GASINSKI LESZEK, PAPAGEORGIOU NIKOLAOS |

Journal | Dynamic Systems and Applications |

Volume | 24 |

Start Page | 523 |

Pagination | 36 |

Date Published | 2015 |

ISSN | 1056-2176 |

AMS Subject Classification | 35J20, 35J60, 35J92, 58E05 |

Abstract | We consider a parametric nonlinear Dirichlet problem driven by the p-Laplacian and with a Carath´eodory reaction which is (p − 1)-superlinear near ±∞ (but without satisfying the Ambrosetti-Rabinowitz condition) and (p − 1)-sublinear near zero. We show that for all values of the parameter λ > 0, the problem has at least three nontrivial solutions (two of constant sign). If we alter the geometry near the origin by introducing a “concave” nonlinearity (problem with combined nonlinearities), we show the existence of at least five nontrivial solutions (four of constant sign and the fifth nodal), when the parameter λ > 0 is small. Also, we produce extremal constant sign solutions u |

https://acadsol.eu/dsa/articles/24/41-DSA-523-558.pdf | |

Refereed Designation | Refereed |