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

We discuss the existence and nonexistence of solution of a nonlinear problem p(x)-elliptic-div(a(x,∇u))+g(x,u,∇u)=μ, where μ is a Radon measure with bounded total variation, by considering the Sobolev spaces with variable exponents. This study is done in two cases: (i) μ is absolutely continuous wit...

Full description

Saved in:
Bibliographic Details
Published in:International journal of analysis 2014-01, Vol.2014 (2014), p.1-15
Main Authors: Azroul, Elhoussine, Barbara, Abdelkrim, Redwane, Hicham
Format: Article
Language:English
Citations: Items that this one cites
Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:We discuss the existence and nonexistence of solution of a nonlinear problem p(x)-elliptic-div(a(x,∇u))+g(x,u,∇u)=μ, where μ is a Radon measure with bounded total variation, by considering the Sobolev spaces with variable exponents. This study is done in two cases: (i) μ is absolutely continuous with respect to p(x)-capacity. and (ii) μ is concentrated on a Borel set of null p(x)-capacity.
ISSN:2314-498X
2314-4998
DOI:10.1155/2014/320527