| Abstract: |
| We prove uniqueness of positive radial solutions to the p-Laplacian problem%
\begin{equation*}
\left\{
\begin{array}{c}
-\Delta _{p}u=\lambda f(u)\ \text{in }\Omega , \
u=0\ \text{on\ }\partial \Omega ,%
\end{array}%
\right.
\end{equation*}%
where $\Delta _p u=div(|\nabla u|^{p-2}\nabla u),~p\geq 2,~\Omega $
is the open unit ball in $R^{N},N>1,~ f:(0,\infty )\rightarrow \mathbb{R}$
is concave, $p~-$ sublinear at $\infty $ with infinite semipositone structure
at $0,$ and $\lambda $ is a large parameter. |
|