Article ID Journal Published Year Pages File Type
4609248 Journal of Differential Equations 2016 31 Pages PDF
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
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