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

Antonio Greco

 Dipartimento di Matematica e Informatica, via Ospedale 72, Cagliari 09124, Italy
Received 24 August 2004; Revised 25 May 2005; Accepted 9 August 2005

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.