The Robin problem for the Henon equation

Authors

  • H. He

Keywords:

H\'{e}non equation, Symmetry breaking, Robin problem, Ground state solutions

Abstract

In this paper, we consider the following Robin problem {−\-Δu=|x|αup x∈Ω,u>0,x∈Ω,∂u∂ν+βu=0x∈∂Ω, where $\Omega$ is the unit ball in $\mathbb{R}^N$ centered at the origin, with $N\geq 3$. $p>1, \,\alpha>0, \beta>0$ and $\nu$ is the unit outward vector normal to $\partial\Omega$. We prove that the above problem has no solution when $\beta$ is small enough. We also obtain existence results and we analysis the symmetry breaking of the ground state solutions. 10.1017/S0004972713000476

Published

2013-07-23

Issue

Vol. 88 No. 1 (2013)

Section

Articles
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