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Journal of Applied Mathematics
Volume 2014 (2014), Article ID 231892, 9 pages
http://dx.doi.org/10.1155/2014/231892
Research Article

Existence of Weak Solutions for Nonlinear Time-Fractional -Laplace Problems

1School of Mathematics and Statistics, Xi’an Jiaotong University, Xi’an 710049, China
2Department of Chemical & Petroleum Engineering, Schulich School of Engineering, University of Calgary, Calgary, AB, Canada T2N 1N4

Received 9 March 2014; Revised 5 June 2014; Accepted 10 June 2014; Published 2 July 2014

Academic Editor: Yansheng Liu

Copyright © 2014 Meilan Qiu and Liquan Mei. 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 weak solution for -Laplace problem is studied in the paper. By exploiting the relationship between the Nehari manifold and fibering maps and combining the compact imbedding theorem and the behavior of Palais-Smale sequences in the Nehari manifold, the existence of weak solutions is established. By means of the Arzela-Ascoli fixed point theorem, some existence results of the corresponding time-fractional equations of the -Laplace problem are obtained.