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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 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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Correspondence to Antonio Greco.

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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