6533b7d4fe1ef96bd12632cc

RESEARCH PRODUCT

Nonlinear Liouville Problems in a Quarter Plane

Chang-lin Xiang

subject

osittaisdifferentiaaliyhtälötPlane (geometry)General MathematicsOpen problemta111010102 general mathematicsMathematical analysis35B09 35B53 35J60Quarter (United States coin)01 natural sciencesNonlinear systemMathematics - Analysis of PDEsSquare root0103 physical sciencesFOS: Mathematicspartial differential equations010307 mathematical physics0101 mathematicsLaplace operatorAnalysis of PDEs (math.AP)Mathematics

description

We answer affirmatively the open problem proposed by Cabr\'e and Tan in their paper "Positive solutions of nonlinear problems involving the square root of the Laplacian" (see Adv. Math. {\bf 224} (2010), no. 5, 2052-2093).

https://doi.org/10.1093/imrn/rnw095