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International Journal of Analysis
Volume 2014 (2014), Article ID 320527, 15 pages
http://dx.doi.org/10.1155/2014/320527
Research Article

Existence and Nonexistence of a Solution for a Nonlinear -Elliptic Problem with Right-Hand Side Measure

1Laboratory LAMA, Department of Mathematics, Faculty of Sciences Dhar El Mahraz, University of Fez, Atlas, 1796 Fez, Morocco
2Faculty of Juridical, Economic and Social Sciences, Hassan 1st University, BP 539, Settat, Morocco

Received 4 November 2013; Accepted 24 February 2014; Published 4 May 2014

Academic Editor: Mats Ehrnstrom

Copyright © 2014 Elhoussine Azroul et al. 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 discuss the existence and nonexistence of solution of a nonlinear problem -elliptic-, where is a Radon measure with bounded total variation, by considering the Sobolev spaces with variable exponents. This study is done in two cases: (i) is absolutely continuous with respect to -capacity. and (ii) is concentrated on a Borel set of null -capacity.