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, <sup>†</sup><b>This contribution is part of the Special Issue:</b> Contemporary PDEs between theory and modeling—Dedicated to Sandro Salsa, on the occasion of his 70th birthday, Guest Editor: Gianmaria Verzini, Link: <a href="www.aimspress.com/mine/article/5753/special-articles" target="_blank">www.aimspress.com/mine/article/5753/special-articles</a>
Abstract
We prove some new results about the growth, the monotonicity and the symmetry of (possibly) unbounded non-negative solutions of -Δ<i>u</i> = <i>f</i> (<i>u</i>) on half-spaces, where <i>f</i> 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.