scholarly journals Properties of positive harmonic functions on the half-space with a nonlinear boundary condition

2010 ◽  
Vol 248 (3) ◽  
pp. 617-637 ◽  
Author(s):  
Emerson Abreu ◽  
João Marcos do Ó ◽  
Everaldo Medeiros
Keyword(s):  
Boundary Condition ◽  
Half Space ◽  
Harmonic Functions ◽  
Nonlinear Boundary ◽  
Nonlinear Boundary Condition ◽  
Positive Harmonic Functions

scholarly journals Nonlinear elliptic equations on the upper half space

2020 ◽  
pp. 2050085
Author(s):  
Sufang Tang ◽  
Lei Wang ◽  
Meijun Zhu
Keyword(s):  
Boundary Condition ◽  
Half Space ◽  
Positive Solutions ◽  
Elliptic Equations ◽  
Symmetric Functions ◽  
Nonlinear Boundary ◽  
Nonlinear Boundary Condition ◽  
Nonlinear Elliptic Equations ◽  
Nonlinear Elliptic

In this paper, we shall classify all positive solutions of [Formula: see text] on the upper half space [Formula: see text] with nonlinear boundary condition [Formula: see text] on [Formula: see text] for parameters [Formula: see text] and [Formula: see text]. We will prove that for [Formula: see text] or [Formula: see text], [Formula: see text] (and [Formula: see text]) all positive solutions are functions of last variable; for [Formula: see text] (and [Formula: see text]) positive solutions must be either some functions depending only on last variable, or radially symmetric functions.

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