On concentration of least energy solutions for magnetic critical Choquard equations

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:464

Article

Mukherjee, T.¹  Sreenadh, K.¹ 

[1] Indian Inst Technol Delhi, Dept Math, New Delhi 110016, India

关键词: Nonlinear Schrodinger equations;    Magnetic potential;    Choquard equation;    Hardy-Littlewood-Sobolev critical exponent;   

DOI  :  10.1016/j.jmaa.2018.04.010

来源: Elsevier

【 摘 要 】

In the present paper, we consider the following magnetic nonlinear Choquard equation { (-i del + A(x))(2)u + mu g(x)u = lambda u + (vertical bar x vertical bar(-alpha) * vertical bar u vertical bar(2*alpha)) vertical bar u vertical bar(2*alpha-2)u in R-n, u is an element of H-1 (R-n, C) where n >= 4, 2*(alpha) = 2n-alpha/n-2, alpha is an element of (0,n), mu > 0, lambda > 0 is a parameter, A(x) : R-n -> R-n is a magnetic vector potential and g(x) is a real valued potential function on R-n. Using variational methods, we establish the existence of least energy solution under some suitable conditions. Moreover, the concentration behavior of solutions is also studied as mu -> +infinity. (C) 2018 Elsevier Inc. All rights reserved.

【 授权许可】

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