期刊
DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS
卷 40, 期 1, 页码 467-489出版社
AMER INST MATHEMATICAL SCIENCES-AIMS
DOI: 10.3934/dcds.2020018
关键词
Weighted Hardy-Littlewood-Sobolev inequality; integral system; existence of positive solution; Serrin-type condition
资金
- National Natural Science Foundation of China [11871278, 11671209]
This paper is concerned with the existence/nonexistence of positive solutions of a weighted Hardy-Littlewood-Sobolev type integral system. Such a system is related to the extremal functions of the weighted Hardy-Littlewood-Sobolev inequality. The Serrin-type condition is critical for existence of positive solutions in L-lo(c)infinity (R-n \ {0}). When the Serrin-type condition does not hold, we prove the nonexistence by an iteration process. In addition, we find three pairs of radial solutions when the Serrin-type condition holds. One is singular, and the other two are integrable in R-n and decaying fast and slowly respectively.
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