Classification of positive solutions to fractional order Hartree equations via a direct method of moving planes

Authors

Wei Dai, Beihang University
Yanqin Fang, University of WollongongFollow
Guolin Qin, Beihang University

RIS ID

126776

Publication Details

Dai, W., Fang, Y. & Qin, G. (2018). Classification of positive solutions to fractional order Hartree equations via a direct method of moving planes. Journal of Differential Equations, 265 (5), 2044-2063.

Abstract

In this paper, we are concerned with the fractional order static Hartree equations with critical nonlocal nonlinearity. We prove that the positive solutions are radially symmetric about some point in R d and must assume the certain explicit forms. The arguments used in our proof is a variant (for nonlocal nonlinearity) of the direct moving plane method for fractional Laplacians in [6]. The main ingredients are the variants (for nonlocal nonlinearity) of the maximum principles, i.e., Decay at infinity and Narrow region principle (Theorem 2.1 and 2.6).