On the solutions to some elliptic equations with nonlinear Neumann boundary conditions

Abstract

We describe all nontrivial nonnegative solutions to the problem $$\begin{cases} -\Delta u = a u^{{n+2}\over{n-2}} \quad &\hbox{in }\ H, \cr {{\partial u }\over {\partial \nu }} = bu^{{n}\over{n-2}} &\hbox{on } \ \partial H, \end{cases}$$ where $H$ is the half space of $\mathbb{R}^n (n\ge3)$.

Article information

Source
Adv. Differential Equations Volume 1, Number 1 (1996), 91-110.

Dates
First available in Project Euclid: 25 April 2013