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Sign-preserving property for some fourth-order elliptic operators in one dimension or in radial symmetry

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Abstract

We show that for a class of one-dimensional linear elliptic fourth-order equations with homogeneous Dirichlet boundary conditions, a non-positive and non-vanishing right-hand side gives rise to a negative solution. We obtain a similar result for the same class of equations for radially symmetric solutions in a ball or in an annulus. We then give several applications, including applications to non-linear equations and eigenvalue problems.

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Authors and Affiliations

  1. Institut de Mathématiques de Toulouse CNRS UMR 5219, Université de Toulouse, F-31062, Toulouse Cedex 9, France

    Philippe Laurençot

  2. Institut für Angewandte Mathematik, Leibniz Universität Hannover, Welfengarten 1, D-30167, Hannover, Germany

    Christoph Walker

Authors
  1. Philippe Laurençot
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  2. Christoph Walker
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Corresponding author

Correspondence to Philippe Laurençot.

Additional information

The work of Ph. L. was partially supported by the Centre International de Mathématiques et d’Informatique CIMI, Toulouse.

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Laurençot, P., Walker, C. Sign-preserving property for some fourth-order elliptic operators in one dimension or in radial symmetry. JAMA 127, 69–89 (2015). https://doi.org/10.1007/s11854-015-0024-2

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  • DOI: https://doi.org/10.1007/s11854-015-0024-2

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