  We investigate the problem $$ \left\{ \begin{array}{ll} -\Delta_p u =
g(u)|\nabla u|^p + f(x,u) \ & \mbox{in} \ \ \Omega, \ \ \\ u>0 \ &\mbox{in} \ \
\Omega, \ \
  u = 0 \ &\mbox{on} \ \ \partial\Omega, \end{array}
  \right. \leqno{(P)} $$ in a bounded smooth domain $\Omega \subset
\mathbb{R}^N$. Using a Kazdan-Kramer change of variable we reduce this problem
to a quasilinear one without gradient term and therefore approachable by
variational methods. In this way we come to some new and interesting problems
for quasilinear elliptic equations which are motivated by the need to solve
$(P)$. Among other results, we investigate the validity of the
Ambrosetti-Rabinowitz condition according to the behavior of $g$ and $f$.
Existence and multiplicity results for $(P)$ are established in several
situations.
