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Abstract and Applied Analysis
Volume 2013, Article ID 398164, 11 pages
http://dx.doi.org/10.1155/2013/398164
Research Article

Existence of Prescribed -Norm Solutions for a Class of Schrödinger-Poisson Equation

1Department of Mathematics, Soochow University, Suzhou, Jiangsu 215006, China
2Cumt College of Sciences, China University of Mining and Technology, Xuzhou, Jiangsu 221116, China

Received 26 May 2013; Accepted 15 July 2013

Academic Editor: Kanishka Perera

Copyright © 2013 Yisheng Huang et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

By using the standard scaling arguments, we show that the infimum of the following minimization problem: −   can be achieved for and small, where . Moreover, the properties of and the associated Lagrange multiplier are also given if .