1.
Adv Nonlinear Stud
; 17(2): 297-310, 2017 May 01.
Artículo
en Inglés
| MEDLINE
| ID: mdl-37727771
RESUMEN
We consider nonnegative solutions to -Δâ¢u=fâ¢(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: fâ¢(0)<0, fâ¢(0)=0 or fâ¢(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.