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We study the existence and nonexistence of positive solutions in the wholeEuclidean space of coercive quasi-linear elliptic equations such as \[ \Delta_pu = f(u)\pm g(\left|\nabla u\right|) \] where $f\in C([0,\infty))$ and $g\inC^{0,1}([0,\infty)) $ are strictly increasing with $ f(0)=g(0)=0$.  Among other things we obtain generalized integral conditions ofKeller-Osserman type. In the particular case of plus sign on the right-handside we obtain that different conditions are needed when $p\geq 2$ or $p\leq2$, due to the degeneracy of the operator.

Existence and nonexistence of positive solutions of quasi-linear elliptic equations with gradient terms