Boundary Value Problems
Volume 2006 (2006), Article ID 80347, 15 pages
doi:10.1155/BVP/2006/80347
Quasi-concavity for semilinear elliptic equations with non-monotone and anisotropic nonlinearities
Dipartimento di Matematica e Informatica, via Ospedale 72, Cagliari 09124, Italy
Received 24 August 2004; Revised 25 May 2005; Accepted 9 August 2005
Copyright © 2006 Antonio Greco. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Abstract
A boundary-value problem for a semilinear elliptic equation in a
convex ring is considered. Under suitable structural conditions,
any classical solution u lying between its (constant) boundary
values is shown to decrease along each ray starting from the
origin, and to have convex level surfaces.