Advances in Differential Equations

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

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

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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


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