%0 Journal Article %T Monotonicity and Symmetry of Nonnegative Solutions to -Delta u = f(u) in Half-Planes and Strips %+ Laboratoire Amiénois de Mathématique Fondamentale et Appliquée - UMR CNRS 7352 (LAMFA) %A Farina, Alberto %A Sciunzi, Berardino %< avec comité de lecture %@ 1536-1365 %J Advanced Nonlinear Studies %I Walter de Gruyter GmbH %V 17 %N 2, SI %P 297-310 %8 2017 %D 2017 %R 10.1515/ans-2017-0010 %Z Mathematics [math]Journal articles %X We consider nonnegative solutions to -Delta u = f(u) in half-planes and strips, under zero Dirichlet boundary condition. Exploiting a rotating and sliding line technique, we prove symmetry and monotonicity properties of the solutions, under very general assumptions on the nonlinearity f. In fact, we provide a unified approach that works in all cases: f(0)< 0, f(0)= 0 or f(0)> 0. Furthermore, we make the effort to deal with nonlinearities f that may be not locally-Lipschitz continuous. We also provide explicit examples showing the sharpness of our assumptions on the nonlinear function f. %G English %L hal-03621417 %U https://u-picardie.hal.science/hal-03621417 %~ CNRS %~ UNIV-PICARDIE %~ INSMI %~ U-PICARDIE %~ LAMFA