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The Scientific World Journal
Volume 2014, Article ID 920537, 10 pages
Research Article

Stability of Nonlinear Dirichlet BVPs Governed by Fractional Laplacian

Faculty of Mathematics and Computer Science, University of Lodz, Banacha 22, 90-238 Lodz, Poland

Received 31 August 2013; Accepted 14 November 2013; Published 2 March 2014

Academic Editors: A. Atangana, A. Kılıçman, S. C. O. Noutchie, S. S. Ray, and A. Secer

Copyright © 2014 Dorota Bors. 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 consider a class of partial differential equations with the fractional Laplacian and the homogeneous Dirichlet boundary data. Some sufficient condition under which the solutions of the equations considered depend continuously on parameters is stated. The application of the results to some optimal control problem is presented. The methods applied in the paper make use of the variational structure of the problem.