6533b855fe1ef96bd12b0a59

RESEARCH PRODUCT

Uniqueness of positive solutions to some nonlinear Neumann problems

Chang-lin XiangChang-lin XiangYouyan Wan

subject

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)AnalysisMathematics

description

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 ) .

yearjournalcountryeditionlanguage
2017-11-01Journal of Mathematical Analysis and Applications
https://doi.org/10.1016/j.jmaa.2017.06.006