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Solutions of perturbed Schrödinger equations with electromagnetic fields and critical nonlinearity

Part of: Partial differential equations Elliptic equations and systems

Published online by Cambridge University Press:  28 October 2010

Sihua Liang  and
Jihui Zhang
Sihua Liang
Affiliation:
Institute of Mathematics, School of Mathematical Sciences, Nanjing Normal University, 210097 Jiangsu, People's Republic of China (liangsihua@163.com) College of Mathematics, Changchun Normal University, Changchun, 130032 Jilin, People's Republic of China (jihuiz@jlonline.com)
Jihui Zhang
Affiliation:
Institute of Mathematics, School of Mathematical Sciences, Nanjing Normal University, 210097 Jiangsu, People's Republic of China (liangsihua@163.com) The Institute of Mathematical Sciences, The Chinese University of Hong Kong, Shatin, NT, Hong Kong
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Abstract

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We consider the existence and multiplicity of standing-wave solutions

of nonlinear Schrödinger equations with electromagnetic fields and critical nonlinearity

Under suitable assumptions, we prove that it has at least one solution and that, for any m ∈ ℕ, it has at least m pairs of solutions.

Keywords

nonlinear Schrödinger equationcritical nonlinearitymagnetic fieldsvariational methods

MSC classification

Secondary: 35J60: Nonlinear elliptic equations 35B33: Critical exponents
Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 54 , Issue 1 , February 2011 , pp. 131 - 147
Copyright
Copyright © Edinburgh Mathematical Society 2010

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