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

Boundary Value Problems volume 2006, Article number: 80347 (2006) Cite this article

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 and Affiliations

  1. Dipartimento di Matematica e Informatica, via Ospedale 72, Cagliari, 09124, Italy

    Antonio Greco

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  1. Antonio Greco
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Correspondence to Antonio Greco.

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Open Access This article is distributed under the terms of the Creative Commons Attribution 2.0 International License ( https://creativecommons.org/licenses/by/2.0 ), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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Greco, A. Quasi-concavity for semilinear elliptic equations with non-monotone and anisotropic nonlinearities. Bound Value Probl 2006, 80347 (2006). https://doi.org/10.1155/BVP/2006/80347

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

Keywords

  • Differential Equation
  • Partial Differential Equation
  • Ordinary Differential Equation
  • Functional Equation
  • Structural Condition