Electron. J. Differential Equations, Vol. 2017 (2017), No. 199, pp. 1-18.

Schrodinger equations with magnetic fields and Hardy-Sobolev critical exponents.

Zhenyu Guo, Michael Melgaard, Wenming Zou

This article is motivated by problems in astrophysics. We consider nonlinear Schrodinger equations and related systems with magnetic fields and Hardy-Sobolev critical exponents. Under proper conditions, existence of ground state solutions to these equations and systems are established.

Submitted May 1, 2016. Published August 11, 2017.
Math Subject Classifications: 35Q55, 35A15, 47J30, 81V10.
Key Words: Ground state; magnetic field; concentration-compactness; Hardy-Sobolev critical exponent

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Zhenyu Guo
School of Sciences
Liaoning Shihua University
Fushun 113001, China
email: guozy@163.com
Michael Melgaard
Department of Mathematics
University of Sussex
Brighton BN1 9QH, Great Britain
email: m.melgaard@sussex.ac.uk
phone +44 (0) 1273 67 8933
Wenming Zou
Department of Mathematical Sciences
Tsinghua University
Beijing 100084, China
email: wzou@math.tsinghua.edu.cn

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