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On concentration of least energy solutions for magnetic critical Choquard equationsPublished in

2018

Volume: 464

Issue: 1

Pages: 402 - 420

In the present paper, we consider the following magnetic nonlinear Choquard equation {(−i∇+A(x))2u+μg(x)u=λu+(|x|−α⁎|u|2⁎ α)|u|2α ⁎−2uinRn,u∈H1(Rn,C) where n≥4, 2α ⁎=[Formula presented], α∈(0,n), μ>0, λ>0 is a parameter, A(x):Rn→Rn is a magnetic vector potential and g(x) is a real valued potential function on Rn. 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 μ→+∞. © 2018 Elsevier Inc.}, author_keywords={Choquard equation; Hardy–Littlewood–Sobolev critical exponent; Magnetic potential; Nonlinear Schrödinger equations}, references={Alves, C.O., Figueiredo, G.M., Multiple solutions for a semilinear elliptic equation with critical growth and magnetic field (2014) Milan J. Math., 82 (2), pp. 389-405; Alves, C.O., Figueiredo, G., Yang, M., Existence of solutions for a nonlinear Choquard equation with potential vanishing at infinity (2016) Adv. 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Phys., 153 (2), pp. 229-244}, correspondence_address1={Sreenadh, K.; Department of Mathematics, Hauz Khaz, India; email: sreenadh@maths.iitd.ernet.in}, publisher={Academic Press Inc.}, issn={0022247X}, language={English}, abbrev_source_title={J. Math. Anal. Appl.}, document_type={Article}, source={Scopus},

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Journal | Journal of Mathematical Analysis and Applications |
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