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2001 Symmetry and nonexistence results for Emden-Fowler equations in cones
Jérôme Busca
Differential Integral Equations 14(8): 897-912 (2001).

Abstract

The purpose of this paper is to state some qualitative properties of the solutions to the Emden-Fowler equation $\Delta u + r^\sigma u^p = 0$ in a cone with Dirichlet boundary conditions. Namely one can show that every solution has the same symmetry as the cone in some sense; furthermore it is possible to extend the nonexistence results for regular solutions to this equation already stated by C. Bandle and M. Essen in [2]. For this one needs to establish some asymptotics for the solutions as $r\rightarrow 0$ or $r\rightarrow \infty$, relying on methods used by Veron in [25] for similar equations, but in different geometries, and then use a special form of the moving-planes method on a sphere in the spirit of [22].

Citation

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Jérôme Busca. "Symmetry and nonexistence results for Emden-Fowler equations in cones." Differential Integral Equations 14 (8) 897 - 912, 2001.

Information

Published: 2001
First available in Project Euclid: 21 December 2012

zbMATH: 1056.35062
MathSciNet: MR1827094

Subjects:
Primary: 35J60
Secondary: 35B05, 35B40, 35B50

Rights: Copyright © 2001 Khayyam Publishing, Inc.

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Vol.14 • No. 8 • 2001
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