In this paper, the authors study the following nonlocal Dirichlet problem: \[ \left\{\begin{aligned} &\left[M\Big(\int_{\Omega} |\nabla u(x)|^p\,dx\Big)\right]^{p-1}\Delta_pu = f(x,u) \quad \text{in } \Omega, \\ &u|_{\partial\Omega} =0, \end{aligned}\right. \] where \(\Omega\) is a bounded domain in \(\mathbb{R}^N\) and \(\Delta_p\) is the \(p\)-Laplacian with \(p>1\). Among the hypothesis, it is assumed that \(f\) satisfies a subcritical growth condition and the Ambrosetti-Rabinowitz condition. Using the Mountain pass Theorem, it is shown that this problem has a solution. The existence of infinitely many solutions is obtained if in addition \(f\) is odd with respect to its second argument. Some examples are given.