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Abstract and Applied Analysis
Volume 2013, Article ID 638425, 9 pages
Research Article

Existence of Solutions for a Fractional Laplacian Equation with Critical Nonlinearity

Department of Mathematics, Zhejiang Normal University, Jinhua 321004, China

Received 5 July 2013; Revised 11 October 2013; Accepted 18 October 2013

Academic Editor: Mihai Mihǎilescu

Copyright © 2013 Zifei Shen and Fashun Gao. 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.


We study the fractional Laplacian equation , , here , , is the critical exponent, and is a real potential function. Employing the variational method we prove the existence of nontrivial solutions for small and large.