期刊论文

Li, Gongbao

英文

Journal of Differential Equations

0022-0396

2019

266

11

7101-7123

10.1016/j.jde.2018.11.024

NSFCNational Natural Science Foundation of China (NSFC) [11501428, 11771166, 11371159]; Hubei Key Laboratory of Mathematical Sciences; Program for Changjiang Scholars and Innovative Research Team in UniversityProgram for Changjiang Scholars & Innovative Research Team in University (PCSIRT) [IRT_17R46]

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In this paper, we study the existence and concentration behavior of minimizers for i(V)(c) = inf (u is an element of Sc) I-V(u), here S-c ={u is an element of H-1(R-N)vertical bar integral(RN) V(x)vertical bar u vertical bar(2) < +infinity, vertical bar u vertical bar(2) = c > 0} and IV(u) =1/2 integral(RN) (a vertical bar del u vertical bar(2)+ V(x)vertical bar u vertical bar(2)) + b/4 (integral(RN)vertical bar del u vertical bar(2))(2) - 1/p integral(RN)vertical bar u vertical bar(p), where N = 1, 2, 3 and a, b > 0 are constants. By the Gagliardo-Nirenberg inequality, we get the sharp existe...