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Abstract and Applied Analysis
Volume 2014 (2014), Article ID 143741, 10 pages
Research Article

On the Existence of Solutions for the Critical Fractional Laplacian Equation in

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

Received 5 May 2013; Accepted 10 December 2013; Published 12 January 2014

Academic Editor: Wenming Zou

Copyright © 2014 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 existence of solutions for the fractional Laplacian equation in , , with critical exponent , , , where has a potential well and is a lower order perturbation of the critical power . By employing the variational method, we prove the existence of nontrivial solutions for the equation.