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- W2945127130 abstract "Abstract In this paper, we prove the existence of entropy solutions for anisotropic elliptic unilateral problem associated to the equations of the form <m:math xmlns:m=http://www.w3.org/1998/Math/MathML><m:mrow><m:mo>-</m:mo><m:munderover><m:mo>∑</m:mo><m:mrow><m:mi>i</m:mi><m:mo>=</m:mo><m:mn>1</m:mn></m:mrow><m:mi>N</m:mi></m:munderover><m:mrow><m:msub><m:mrow><m:mo>∂</m:mo></m:mrow><m:mi>i</m:mi></m:msub><m:msub><m:mrow><m:mi>a</m:mi></m:mrow><m:mi>i</m:mi></m:msub><m:mo>(</m:mo><m:mi>x</m:mi><m:mo>,</m:mo><m:mi>u</m:mi><m:mo>,</m:mo><m:mo>∇</m:mo><m:mi>u</m:mi><m:mo>)</m:mo><m:mo>-</m:mo></m:mrow><m:munderover><m:mo>∑</m:mo><m:mrow><m:mi>i</m:mi><m:mo>=</m:mo><m:mn>1</m:mn></m:mrow><m:mi>N</m:mi></m:munderover><m:mrow><m:msub><m:mrow><m:mo>∂</m:mo></m:mrow><m:mi>i</m:mi></m:msub><m:msub><m:mrow><m:mi>φ</m:mi></m:mrow><m:mi>i</m:mi></m:msub><m:mo>(</m:mo><m:mi>u</m:mi><m:mo>)</m:mo><m:mo>=</m:mo><m:mi>f</m:mi><m:mo>,</m:mo></m:mrow></m:mrow></m:math> $$ - sumlimits_{i = 1}^N {{partial _i}{a_i}(x,u,nabla u) - } sumlimits_{i = 1}^N {{partial _i}{phi _i}(u) = f,} $$ where the right hand side f belongs to L 1 (Ω). The operator <m:math xmlns:m=http://www.w3.org/1998/Math/MathML><m:mrow><m:mo>-</m:mo><m:msubsup><m:mo>∑</m:mo><m:mrow><m:mi>i</m:mi><m:mo>=</m:mo><m:mn>1</m:mn></m:mrow><m:mi>N</m:mi></m:msubsup><m:mrow><m:msub><m:mrow><m:mo>∂</m:mo></m:mrow><m:mi>i</m:mi></m:msub><m:msub><m:mrow><m:mi>a</m:mi></m:mrow><m:mi>i</m:mi></m:msub><m:mrow><m:mo>(</m:mo><m:mrow><m:mi>x</m:mi><m:mo>,</m:mo><m:mi>u</m:mi><m:mo>,</m:mo><m:mo>∇</m:mo><m:mi>u</m:mi></m:mrow><m:mo>)</m:mo></m:mrow></m:mrow></m:mrow></m:math> $- sumnolimits_{i = 1}^N {{partial _i}{a_i}left( {x,u,nabla u} right)} $ is a Leray-Lions anisotropic operator and ϕ i ∈ C 0 (ℝ,ℝ)." @default.
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- W2945127130 date "2018-12-01" @default.
- W2945127130 modified "2023-10-14" @default.
- W2945127130 title "Existence of Solutions for Some Nonlinear Elliptic Anisotropic Unilateral Problems with Lower Order Terms" @default.
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- W2945127130 doi "https://doi.org/10.1515/mjpaa-2018-0014" @default.
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