Some properties of solutions for a nonlinear integral system

Abstract

Abstract In this paper, a nonlinear integral system is considered in critical space. Some important properties of positive solutions such as symmetry, monotonicity, integrability, and asymptotic behaviors, are obtained. Moreover, by comparison and analysis, we discover that those properties are an important tool to characterize the tightness of the system.

Keywords

• integral system
• regularity lifting lemma
• weighted Hardy-Littlewood-Sobolev inequality