In this chapter we determine a priori estimates on the behavior at infinity of positive solutions of the equation $$ \Delta u + a(x)u-b(x)u^{\sigma} \geq 0, \,\,\,\, \sigma > 1 $$ (4.1) on M under assumptions on \( a(x) \) and \( b(x) \) related to the geometrical requirement $$ \mathrm{Ric} \geq-(m-1)H^{2}(1+r(x)^{2})^{\frac{\delta}{2}} $$ (4.2) for some\( H > 0 \) and \( \delta\,\, \epsilon\,\, \mathbb{R} \).