  We prove nonexistence of nonconstant global minimizers with limit at infinity
of the semilinear elliptic equation $-\Delta u=f(u)$ in the whole $R^N$, where
$f\in C^1(R)$ is a general nonlinearity and $N\geq 1$ is any dimension. As a
corollary of this result, we establish nonexistence of nonconstant bounded
radial global minimizers of the previous equation.
