Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4609248 | Journal of Differential Equations | 2016 | 31 Pages |
Abstract
In this paper we classify the isolated singularities of positive solutions to Choquard equation−Δu+u=Iα[up]uqinRN∖{0},lim|x|→+∞u(x)=0, where p>0,q≥1,N≥3,α∈(0,N)p>0,q≥1,N≥3,α∈(0,N) and Iα[up](x)=∫RNu(y)p|x−y|N−αdy. We show that any positive solution u is a solution of−Δu+u=Iα[up]uq+kδ0inRN in the distributional sense for some k≥0k≥0, where δ0δ0 is the Dirac mass at the origin. We prove the existence of singular solutions in the subcritical case: p+q
Related Topics
Physical Sciences and Engineering
Mathematics
Analysis
Authors
Huyuan Chen, Feng Zhou,