## Advances in Differential Equations

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

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

M. Chipot, M. Fila, and I. Shafrir

#### 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

**Permanent link to this document**

https://projecteuclid.org/euclid.ade/1366896316

**Mathematical Reviews number (MathSciNet)**

MR1357956

**Zentralblatt MATH identifier**

0839.35042

**Subjects**

Primary: 35J65: Nonlinear boundary value problems for linear elliptic equations

#### Citation

Chipot, M.; Shafrir, I.; Fila, M. On the solutions to some elliptic equations with nonlinear Neumann boundary conditions. Adv. Differential Equations 1 (1996), no. 1, 91--110. https://projecteuclid.org/euclid.ade/1366896316