Boundary Value Problems

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Quasi-concavity for semilinear elliptic equations with non-monotone and anisotropic nonlinearities

Boundary Value Problems20062006:80347

https://doi.org/10.1155/BVP/2006/80347

©  Antonio Greco 2006

Received: 24 August 2004

Accepted: 9 August 2005

Published: 14 February 2006

Abstract

A boundary-value problem for a semilinear elliptic equation in a convex ring is considered. Under suitable structural conditions, any classical solution lying between its (constant) boundary values is shown to decrease along each ray starting from the origin, and to have convex level surfaces.

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Authors’ Affiliations

(1)
Dipartimento di Matematica e Informatica

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Copyright

© Antonio Greco 2006

This article is published under license to BioMed Central Ltd. 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.