A supercritical scalar field equation with a forcing term
A supercritical scalar field equation with a forcing term
复制标题
DOI：
10.1016/j.matpur.2019.04.003
复制
发表时间：
2019-02
期刊：
影响因子：
--
通讯作者：
Kazuhiro Ishige;S. Okabe;Tokushi Sato
中科院分区：
文献类型：
--
作者：
Kazuhiro Ishige;S. Okabe;Tokushi Sato
本文关注 R N 中具有强迫项− Δ u+ u= u p+ κ μ 的标量场方程的椭圆问题，其中 N≥ 2、p> 1、κ> 0 且 μ 是 R N 中具有紧支撑的氡测度。在μ上合适的可积条件下，我们给出了在1< p< p J L的情况下，存在和不存在在空间无限衰减的正解的完整分类。这里p J L是所谓的Joseph-Lundgren指数。
This paper is concerned with the elliptic problem for a scalar field equation with a forcing term− Δ u+ u= u p+ κ μ in R N, where N≥ 2, p> 1, κ> 0 and μ is a Radon measure in R N with a compact support. Under a suitable integrability condition on μ, we give a complete classification of the existence and nonexistence of positive solutions decaying at the space infinity in the case of 1< p< p J L. Here p J L is the so-called Joseph-Lundgren exponent.