  We discuss the occurrence of positive solutions which decay to 0 as $|
x|\to+\infty$ to the differential equation $\Delta u+f(x,u)+g(| x|)x\cdot\nabla
u=0$, $| x|>R>0$, $x\in\mathbb{R}^{n}$, where $n\geq 3$, $g$ is nonnegative
valued and $f$ has alternating sign, by means of the comparison method. Our
results complement several recent contributions from [M. Ehrnstr\"{o}m, O.G.
Mustafa, On positive solutions of a class of nonlinear elliptic equations,
Nonlinear Anal. TMA 67 (2007), 1147--1154].
