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BY-NC-ND 3.0 license Open Access Published by De Gruyter August 5, 2014

Multivalued problem with Robin boundary condition involving diffuse measure data and variable exponent

  • Stanislas Ouaro EMAIL logo , Arouna Ouedraogo and Safimba Soma

Abstract

We study a nonlinear elliptic problem with Robin type boundary condition, governed by a general Leray–Lions operator with variable exponents and diffuse Radon measure data which does not charge the sets of zero p(·)-capacity. We prove an existence and uniqueness result of a weak solution.

MSC: 35K55; 35D05

This work was done within the framework of the visit of the authors at the Abdus Salam International Centre for Theoretical Physics (ICTP), Trieste, Italy. The authors thank the Mathematics Section of ICTP for their hospitality and for financial support and all facilities. The authors also want to thank the anonymous referee for is valuable comments on the paper.

Received: 2014-1-31
Revised: 2014-7-19
Accepted: 2014-7-20
Published Online: 2014-8-5
Published in Print: 2014-11-1

© 2014 by De Gruyter

This article is distributed under the terms of the Creative Commons Attribution Non-Commercial License, which permits unrestricted non-commercial use, distribution, and reproduction in any medium, provided the original work is properly cited.

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