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A Liouville-type theorem for the Lane-Emden equation in a half-space

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 Added by Philippe Souplet
 Publication date 2020
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and research's language is English




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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.



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