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

Autor:	Dupaigne, Louis, Sirakov, Boyan, Souplet, Philippe
Rok vydání:	2020
Předmět:	Mathematics - Analysis of PDEs
Druh dokumentu:	Working Paper
Popis:	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. Comment: 14 pages. arXiv admin note: text overlap with arXiv:2002.07247
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2003.11466 Zobrazit plný text záznamu View this record from Arxiv