Search results for "Liouville type theorem"

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Uniqueness of positive solutions to some nonlinear Neumann problems

2017

Abstract Using the moving plane method, we obtain a Liouville type theorem for nonnegative solutions of the Neumann problem { div ( y a ∇ u ( x , y ) ) = 0 , x ∈ R n , y > 0 , lim y → 0 + ⁡ y a u y ( x , y ) = − f ( u ( x , 0 ) ) , x ∈ R n , under general nonlinearity assumptions on the function f : R → R for any constant a ∈ ( − 1 , 1 ) .

Pure mathematicsApplied Mathematicsta111010102 general mathematicsMathematical analysisNeumann problemmoving plane methodFunction (mathematics)Type (model theory)01 natural sciencesNonlinear systemLiouville type theorem0103 physical sciencespartial differential equationsNeumann boundary conditionMoving plane010307 mathematical physicsUniqueness0101 mathematicsConstant (mathematics)AnalysisMathematicsJournal of Mathematical Analysis and Applications
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Uniqueness of positive solutions to some Nonlinear Neumann Problems

2017

Using the moving plane method, we obtain a Liouville type theorem for nonnegative solutions of the Neumann problem ⎧ ⎨ ⎩ div (ya∇u(x, y)) = 0, x ∈ Rn,y > 0, lim y→0+yauy(x, y) = −f(u(x, 0)), x ∈ Rn, under general nonlinearity assumptions on the function f : R → R for any constant a ∈ (−1, 1). peerReviewed

osittaisdifferentiaaliyhtälötLiouville type theoremNeumann problemmoving plane method
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