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## Abstract

This paper is concerned with qualitative properties of solutions to nonlocal reaction–diffusion equations of the form ∫ _{ R N/K } J(x-y)(u(y)-u(x))dy+f(u(x))=0, x∈R ^{N/K} set in a perforated open set R ^{N/K} , where K ⊂ R _{N} is a bounded compact ‘obstacle’ and f is a bistable nonlinearity. When K is convex, we prove some Liouville-type results for solutions satisfying some asymptotic limiting conditions at infinity. We also establish a robustness result, assuming slightly relaxed conditions on K.

Original language | English |
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Pages (from-to) | 291-328 |

Number of pages | 38 |

Journal | Proceedings of the London Mathematical Society |

Volume | 119 |

Issue number | 5 |

Early online date | 7 Feb 2019 |

DOIs | |

Publication status | Published - Aug 2019 |

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Dive into the research topics of 'Liouville type results for a nonlocal obstacle problem'. Together they form a unique fingerprint.## Projects

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