We study a multiplicity result for the perturbed $p$ -Laplacian equation $-\Delta_pu -\lambda g(x)|u|^{p-2}u = f(x,u) + h(x)\mathrm{in}\mathbb{R}^N$ , where $1 < p < N$ and $\lambda$ is near $\lambda_1$ , the principal eigenvalue of the weighted eigenvalue problem $-\Delta_pu = \lambda g|u|^{p-2}u$ in $\mathbb{R}^N$ . Depending on which side $\lambda$ is from $\lambda_1$ , we prove the existence of one or three solutions. This kind of result was firstly obtained by Mawhin and Schmitt (1990) for a semilinear two-point boundary value problem.