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Abstract and Applied Analysis
Volume 2014 (2014), Article ID 809769, 7 pages
http://dx.doi.org/10.1155/2014/809769
Research Article

Three Weak Solutions for Nonlocal Fractional Laplacian Equations

Department of Mathematics, Huaiyin Normal University, Huaian, Jiangsu 223300, China

Received 16 September 2013; Revised 19 November 2013; Accepted 27 November 2013; Published 16 January 2014

Academic Editor: Salvatore A. Marano

Copyright © 2014 Dandan Yang and Chuanzhi Bai. 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

The existence of three weak solutions for the following nonlocal fractional equation in in is investigated, where is fixed, is the fractional Laplace operator, and are real parameters, is an open bounded subset of , , and the function satisfies some regularity and natural growth conditions. The approach is based on a three-critical-point theorem for differential functionals.