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Bibliographic Details
Main Authors: Dupaigne, Louis, Sirakov, Boyan, Souplet, Philippe
Format: Preprint
Published: 2020
Subjects:
Online Access:https://arxiv.org/abs/2003.11466
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Table of Contents:
  • We prove that the Dirichlet problem for the Lane-Emden equation in a half-space has no positive solution which is monotone in the normal direction. As a consequence, this problem does not admit any positive classical solution which is bounded on finite strips. This question has a long history and our result solves a long-standing open problem. Such a nonexistence result was previously available only for bounded solutions, or under a restriction on the power in the nonlinearity. The result extends to general convex nonlinearities.