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

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.