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On classical solutions to the Hartree equation

Authors: 

Phuong Le

Source title: 
Journal of Mathematical Analysis and Applications, 485: 123859, 2020 (ISI)
Academic year of acceptance: 
2019-2020
Abstract: 

This paper is concerned with positive classical solutions to the Hartree equation 

a

. When n ≤ 2, we show that the equation has no positive solution. When ≥ 3, we prove that the equation has no positive solution if a, we also classify all positive solutions to the equation in the critical case a. The main novelty of this paper is that we cover the full range 0 α n and a in our results.