Uniqueness of positive solutions to some Nonlinear Neumann Problems
Wan, Y., & Xiang, C. (2017). Uniqueness of positive solutions to some Nonlinear Neumann Problems. Journal of Mathematical Analysis and Applications, 455 (2), 1835-1847. doi:10.1016/j.jmaa.2017.06.006
Published inJournal of Mathematical Analysis and Applications
© 2017 Elsevier Inc. This is a final draft version of an article whose final and definitive form has been published by Elsevier. Published in this repository with the kind permission of the publisher.
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).