Nonexistence and optimal decay of supersolutions to Choquard equations in exterior domains
Nonexistence and optimal decay of supersolutions to Choquard equations in exterior domains
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DOI：
10.1016/j.jde.2012.12.019
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发表时间：
2012-03
影响因子：
2.4
通讯作者：
Vitaly Moroz;Jean Van Schaftingen
中科院分区：
文献类型：
--
作者：
Vitaly Moroz;Jean Van Schaftingen
考虑一类半线性椭圆问题，其非线性项为幂和幂的Riesz势的乘积。这个方程族包括Choquard或非线性薛定谔-牛顿方程。我们证明了对于某些参数值，方程在外部区域不存在非平凡的非负上解。当存在超解时，同样的技术产生最优的衰减率。
We consider a semilinear elliptic problem with a nonlinear term which is the product of a power and the Riesz potential of a power. This family of equations includes the Choquard or nonlinear Schrödinger–Newton equation. We show that for some values of the parameters the equation does not have nontrivial nonnegative supersolutions in exterior domains. The same techniques yield optimal decay rates when supersolutions exist.