Positive solutions to integral systems with weight and Bessel potentials

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:418

Article

Yin, Hui¹  Lu, Zhongxue¹ 

[1] Jiangsu Normal Univ, Sch Math Sci, Xuzhou 221116, Peoples R China

关键词: Bessel potential;    Integral system;    Integrability Radial symmetry;    Method of moving planes;    Decay rates;   

DOI  :  10.1016/j.jmaa.2014.03.076

来源: Elsevier

【 摘 要 】

In this paper, we consider the integral system with weight and the Bessel potentials: u(x) = f ga(x Y)u(Y)Pv(Y)q dy, Rn V(X) = f ga M Y)v(Y)Puq dy, R. where u,v > 0, o- 0, 0 < n, p q = v 2 and ga(x) is the Bessel potential of order a. First, we get the integrability by regularity lifting lemma. Then we also establish the regularity of the positive solutions. Afterwards, by the method of moving planes in integral forms, we show that the positive solutions are radially symmetric and monotone decreasing about the origin. Finally, by an extension of the idea of Lei [14] and analytical techniques, we get the decay rates of solutions when lxi oo. 2014 Elsevier Inc. All rights reserved.

【 授权许可】

Free