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

Chipot, M; Shafrir, I; Fila, M (1996). On the solutions to some elliptic equations with nonlinear Neumann boundary conditions. Advances in Differential Equations, 1(1):91-110.

## Abstract

We describe all nontrivial nonnegative solutions to the problem $-\Delta u=au^{(n+2)/(n-2)}$ in $H,\ \partial u/\partial\nu=bu^{n/(n-2)}$ on $\partial H$, where $H$ is a half-space of ${\bf R}^n\ (n\geq3)$.

## Abstract

We describe all nontrivial nonnegative solutions to the problem $-\Delta u=au^{(n+2)/(n-2)}$ in $H,\ \partial u/\partial\nu=bu^{n/(n-2)}$ on $\partial H$, where $H$ is a half-space of ${\bf R}^n\ (n\geq3)$.

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