Existence of positive solutions to a Laplace equation with nonlinear boundary condition

2015 ◽  
Vol 66 (6) ◽  
pp. 3061-3083 ◽  
Author(s):  
C.-G. Kim ◽  
Z.-P. Liang ◽  
J.-P. Shi
Keyword(s):  
Boundary Condition ◽  
Positive Solutions ◽  
Laplace Equation ◽  
Nonlinear Boundary ◽  
Nonlinear Boundary Condition ◽  
Existence Of Positive Solutions

scholarly journals First-Order Boundary Value Problem with Nonlinear Boundary Condition on Time Scales

2011 ◽  
Vol 2011 ◽  
pp. 1-8 ◽  
Author(s):  
Ya-Hong Zhao
Keyword(s):  
Boundary Condition ◽  
Boundary Value Problem ◽  
Dynamic Equation ◽  
Iteration Method ◽  
Nonlinear Boundary ◽  
Nonlinear Boundary Condition ◽  
Iterative Schemes ◽  
First Order ◽  
Monotone Iteration ◽  
Existence Of Positive Solutions

This work is concerned with the following first-order dynamic equation on time scale, xΔ(t)+p(t)x(σ(t))=f(t,x(t)),  t∈[0,T]𝕋with the nonlinear boundary conditionx(0)=g(x(σ(T))). By applying monotone iteration method, we not only obtain the existence of positive solutions, but also establish iterative schemes for approximating the solutions.

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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