Groundstates for Choquard equations with the upper critical exponent

Xinfu Li; Shiwang Ma

Groundstates for Choquard equations with the upper critical exponent

Analysis of PDEs 2018-12-17 v1

Authors: Xinfu Li , Shiwang Ma

Abstract

In this paper, an autonomous Choquard equation with the upper critical exponent is considered. By using the Poho\v{z}aev constraint method, the subcritical approximation method and the compactness lemma of Strauss, a groundstate solution in $H^1(\mathbb{R}^N)$ which is positive and radially symmetric is obtained. The result here extends and complements the earlier theorems.

Keywords

choquard equation upper critical exponent groundstate solution pohožaev constraint strauss lemma radial symmetry

Cite

@article{arxiv.1812.05761,
  title  = {Groundstates for Choquard equations with the upper critical exponent},
  author = {Xinfu Li and Shiwang Ma},
  journal= {arXiv preprint arXiv:1812.05761},
  year   = {2018}
}

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