Affiliation:
1. Institute of Mathematics, School of Mathematical Sciences Nanjing Normal University Nanjing 210023 China
2. College of Information Engineering Nanjing Xiaozhuang University Nanjing 211171 China
Abstract
In this paper, we are concerned with an integral system
where
. Base on the integrability of positive solutions, we obtain some Liouville theorems and the decay rates of positive solutions at infinity. In addition, we use the properties of the contraction map and the shrinking map to prove that
is Lipschitz continuous. In particular, the Serrin type condition is established, which plays an important role to classify the positive solutions.
Funder
National Natural Science Foundation of China
Subject
General Engineering,General Mathematics