  We consider the following problem
  $$(P)
  \begin{cases}
  -\Delta_{p}u= c(x)|u|^{q-1}u+\mu |\nabla u|^{p}+h(x) & \ \ \mbox{ in }\Omega,
  u=0 & \ \ \mbox{ on } \partial\Omega,
  \end{cases}$$
  where $\Omega$ is a bounded set in $\mathbb{R}^{N}$ ($N\geq 3$) with a smooth
boundary, $1<p<N$, $q>0$, $\mu \in \mathbb{R}^{*}$, and $c$ and $ h$ belong to
$L^{k}(\Omega)$ for some $k>\frac{N}{p}$. In this paper, we assume that
$c\gneqq 0$ a.e. in $\Omega$ and $h$ without sign condition, then
  we prove the existence of at least two bounded solutions under the condition
that $\|c\|_{k}$ and $\|h\|_{k}$ are suitably small. For this purpose, we use
the Mountain Pass theorem, on an equivalent problem to $(P)$ with variational
structure. Here, the main difficulty is that the nonlinearity term considered
does not satisfy Ambrosetti and Rabinowitz condition. The key idea is to
replace the former condition by the \textbf{nonquadraticity condition at
infinity}.
