  We use comparison principles, variational arguments and a truncation method
to obtain positive solutions to logistic type equations with harvesting both in
$\mathbb{R}^N$ and in a bounded domain $\Omega\subset\mathbb{R}^N$, with $N\geq
3$, when the carrying capacity of the environment is not constant. By relaxing
the growth assumption on the coefficients of the differential equation we
derive a new equation which is easily solved. The solution of this new equation
is then used to produce a positive solution of our original problem.
