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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

international journal of analysis

Existence and Nonexistence of a Solution for a Nonlinear <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M1"><mml:mi>p</mml:mi><mml:mo stretchy="false">(</mml:mo><mml:mi>x</mml:mi><mml:mo stretchy="false">)</mml:mo></mml:math>-Elliptic Problem with Right-Hand Side Measure

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