期刊
NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS
卷 67, 期 5, 页码 1445-1456出版社
PERGAMON-ELSEVIER SCIENCE LTD
DOI: 10.1016/j.na.2006.07.029
关键词
Maxwell-Schrodinger; standing waves; Palais-Smale sequence
In this paper we study the existence and the multiplicity of standing wave solutions for the nonlinear Schrodinger equation coupled with the Maxwell equations. It seems difficult to obtain a boundedness of a Palais-Smale sequence for the functional associated with this system. We overcome this difficulty by Jeanjean's result [L. Jeanjean, On the existence of bounded Palais-Smale sequence and application to a Landesman-Lazer type problem set on R-N, Proc. Roy. Soc. Edinburgh Sect. A 129 (1999) 787-809], which generalizes Struwe's argument [M. Struwe, Variational Methods, 2nd ed., Springer, 1996; M. Struwe, The existence of a surface of constant mean curvature with free boundaries, Acta Math. 160 (1988) 19-64] and Zou's result [W. Zou, Variant fountain theorem and their applications, Manuscripta Math. 104 (2001) 343-358]. (C) 2006 Elsevier Ltd. All rights reserved.
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