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Some results about semilinear elliptic problems on half-spaces

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

This contribution is part of the Special Issue: Contemporary PDEs between theory and modeling—Dedicated to Sandro Salsa, on the occasion of his 70th birthday
Guest Editor: Gianmaria Verzini
Link: www.aimspress.com/mine/article/5753/special-articles

Special Issues: Contemporary PDEs between theory and modeling—Dedicated to Sandro Salsa, on the occasion of his 70th birthday

We prove some new results about the growth, the monotonicity and the symmetry of (possibly) unbounded non-negative solutions of −∆u = 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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Keywords 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. Mathematics in Engineering, 2020, 2(4): 709-721. doi: 10.3934/mine.2020033


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