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In this note, we prove that least energy solutions of the two-dimensional Henon equation \begin{eqnarray*} -\Delta u = |x|^{2\alpha} u^p \quad x \in \Omega, \quad u 0 \quad x \in \Omega, \quad u = 0 \quad x \in \partial \Omega, \end{eqnarray*} where $\Omega$ is a smooth bounded domain in $R^2$ with $0 \in \Omega$, $\alpha \ge 0$ is a constant and $p >1$, have only one global maximum point when $\alpha > e-1$ and the nonlinear exponent $p$ is sufficiently large. This answers positively to a recent conjecture by C. Zhao (preprint, 2011).

On the number of maximum points of least energy solution to a two-dimensional Hénon equation with large exponent