Some results about semilinear elliptic problems on half-spaces

Alberto Farina; Alberto Farina

doi:10.3934/mine.2020033

Mathematics in Engineering

2020, Volume 2, Issue 4: 709-721. doi: 10.3934/mine.2020033

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Some results about semilinear elliptic problems on half-spaces

Alberto Farina ^,

LAMFA, CNRS UMR 7352, Université de Picardie Jules Verne, 33 rue Saint-Leu, 80039 Amiens, France

Received: 23 December 2019 Accepted: 20 May 2020 Published: 18 June 2020

We prove some new results about the growth, the monotonicity and the symmetry of (possibly) unbounded non-negative solutions of -Δu = f (u) on half-spaces, where f is merely a locally Lipschitz continuous function. Our proofs are based on a comparison principle for solutions of semilinear problems on unbounded slab-type domains and on the moving planes method.
- qualitative properties of solutions to semilinear elliptic equations,
- moving planes method,
- comparison principle
Citation: Alberto Farina. Some results about semilinear elliptic problems on half-spaces[J]. Mathematics in Engineering, 2020, 2(4): 709-721. doi: 10.3934/mine.2020033

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Abstract

We prove some new results about the growth, the monotonicity and the symmetry of (possibly) unbounded non-negative solutions of -Δu = f (u) on half-spaces, where f is merely a locally Lipschitz continuous function. Our proofs are based on a comparison principle for solutions of semilinear problems on unbounded slab-type domains and on the moving planes method.

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