期刊
COMMUNICATIONS ON PURE AND APPLIED ANALYSIS
卷 20, 期 6, 页码 2237-2256出版社
AMER INST MATHEMATICAL SCIENCES-AIMS
DOI: 10.3934/cpaa.2021065
关键词
exterior domain; variational and toplogical methods; Choquard equation
资金
- Research Foundation of Education Bureau of Hubei Province, China [Q20192505]
- NSFC [11771342]
This work proves the existence of at least one positive solution to the Choquard equation using variational and topological methods, as well as establishes a nonlocal version of global compactness result in an unbounded domain.
This work concerns with the following Choquard equation { -Delta u + u = (integral(Omega) u(2) (y)/vertical bar x -y vertical bar(N) (-2) dy)u in Omega, u is an element of H-0(1) ( Omega), where Omega subset of R-N is an exterior domain with smooth boundary. We prove that the equation has at least one positive solution by variational and toplogical methods. Moreover, we establish a nonlocal version of global compactness result in unbounded domain.
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