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Abstract and Applied Analysis
Volume 2013 (2013), Article ID 295480, 9 pages
http://dx.doi.org/10.1155/2013/295480
Research Article

Existence and Uniqueness of Positive Solution for a Fractional Dirichlet Problem with Combined Nonlinear Effects in Bounded Domains

1Mathematics Department, College of Sciences, King Saud University, P.O. Box 2455, Riyadh 11451, Saudi Arabia
2Mathematics Department, College of Sciences and Arts, King Abdulaziz University, Rabigh Campus, P.O. Box 344, Rabigh 21911, Saudi Arabia

Received 20 February 2013; Accepted 10 July 2013

Academic Editor: Daniel C. Biles

Copyright © 2013 Imed Bachar and Habib Mâagli. 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

We prove the existence and uniqueness of a positive continuous solution to the following singular semilinear fractional Dirichlet problem , in where is a bounded -domain in and denotes the Euclidian distance from to the boundary of The nonnegative weight functions are required to satisfy certain hypotheses related to the Karamata class. We also investigate the global behavior of such solution.