Journal
COMMUNICATIONS ON PURE AND APPLIED ANALYSIS
Volume 16, Issue 2, Pages 493-512Publisher
AMER INST MATHEMATICAL SCIENCES-AIMS
DOI: 10.3934/cpaa.2017025
Keywords
Multi-peak solutions; Choquard equation; semiclassical states; penalization arguments; Berestycki-Lions conditions
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Funding
- NSFC [11671364, 11271331, 11571317, 11271360, 11471330]
- ZJNSF [LY15A010010]
- Science Foundation of Chongqing Jiaotong University [15JDKJC-B033]
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In this paper, we study a class of nonlinear Choquard type equations involving a general nonlinearity. By using the method of penalization argument, we show that there exists a family of solutions having multiple concentration regions which concentrate at the minimum points of the potential V. Moreover, the monotonicity of f(s)/s and the so-called Ambrosetti-Rabinowitz condition are not required.
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