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arXiv · 1303.2237

Sign-Preserving Property for Some Fourth-Order Elliptic Operators in One Dimension and Radial Symmetry

Philippe Laurencot·Christoph Walker
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Abstract

For a class of one-dimensional linear elliptic fourth-order equations with homogeneous Dirichlet boundary conditions it is shown that a non-positive and non-vanishing right-hand side gives rise to a negative solution. A similar result is obtained for the same class of equations for radially symmetric solutions in a ball or in an annulus. Several applications are given, including applications to nonlinear equations and eigenvalue problems.

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Philippe Laurencot, Christoph Walker. 2013-03-09. Sign-Preserving Property for Some Fourth-Order Elliptic Operators in One Dimension and Radial Symmetry. https://arxiv.org/abs/1303.2237

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