\(Summary\): In this paper, we consider the following Dirichlet problem for the \(p\)-Laplacian in the positive parameters \(\lambda \) and \(\beta\):
\[\begin{cases}\Delta_p u=\lambda h(x,u)+\beta f(x,u,\nabla)\quad&\text{in }\Omega,\\ u=0&\text{on }\partial\Omega, \end{cases} \]where \(h\), \(f\) are continuous nonlinearities satisfying \(0\le \omega_1(x)u^{q-1}\le h(x,u)\le \omega_2(x)u^{q-1}\) with \(1<q<p\) and \(0\le f(x,u,v)\le\omega_3(x)uâ\vert v\vert^b\), with \(a,b>0\), and \(\Omega\) is a bounded domain of \(\mathbb R^N\), \(N\ge 2\). The functions \(\omega_i\), \(1\le i\le 3\), are positive, continuous weights in \(\overline\Omega\). We prove that there exists a region \( \mathcal D\) in the \(\lambda\beta\)-plane where the Dirichlet problem has at least one positive solution. The novelty in this paper is that our result is valid for nonlinearities with growth higher than \(p\) in the gradient variable.