  We consider the following problem $ -\Delta_{p}u= h(x,u) \mbox{ in }\Omega$,
$u\in W^{1,p}_{0}(\Omega)$, where $\Omega$ is a bounded domain in
$\mathbb{R}^{N}$, $1<p<N$, with a smooth boundary. In this paper we assume that
$h(x,u)=a(x)f(u)+b(x)g(u)$ such that $f$ is regularly varying of index $p-1$
and superlinear at infinity. The function $g$ is a $p$-sublinear function at
zero. The coefficients $a$ and $b$ belong to $L^{k}(\Omega)$ for some
$k>\frac{N}{p}$ and they are without sign condition. Firstly, we show a priori
bound on solutions, then by using variational arguments, we prove the existence
of at least two nonnegative solutions. One of the main difficulties is that the
nonlinearity term $h(x,u)$ does not satisfy the standard Ambrosetti and
Rabinowitz condition.
