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

$- Δ u = (\frac{1}{| x |^{n - α}} ⁎ u^{p}) u^{p - 1} in R^{n} .$ $<![CDATA[// ><!]]>$ When n $n \leq 2$ $<![CDATA[// ><!]]>$ , we show that the equation has no positive solution. When n $n \geq 3$ $<![CDATA[// ><!]]>$ , we prove that the equation has no positive solution if , we also classify all positive solutions to the equation in the critical case . The main novelty of this paper is that we cover the full range 0 $0 < α < n$ $<![CDATA[// ><!]]>$ and in our results.

Link:

https://www.sciencedirect.com/science/article/abs/pii/S0022247X20300214

Publications

On classical solutions to the Hartree equation