| Abstract: |
| We prove uniqueness of positive solutions to the BVP
$\begin{equation*}
\left\{
\begin{array}{c}
-\Delta u=\lambda f(u)\ \text{\ in }\Omega , \
\frac{\partial u}{\partial n}+bu=0\ \text{\ on }\partial \Omega ,%
\end{array}%
\right.
\end{equation*}$
when the parameter $\lambda $ is large independent of $b\in \mathbb{(}%
0,\infty )$. Here $\Omega $ is a bounded domain in $\mathbb{R}^{n}$ with
smooth boundary $\partial \Omega ,\ f:[0,\infty )\rightarrow \mathbb{[}%
0,\infty )\mathbb{\ }$is continuous, sublinear at $\infty $, and satisfies a
concavity-like condition for $u$ large. |
|