We study the following bifurcation problem in any bounded
domain $\Omega$ in $\mathbb{R}^N$ : $$\begin{cases}A_pu := -\sum^N_{i,j=1}\frac{\partial}{\partial x_i}[(\sum^N_{m,k=1}a_{mk}(x)\frac{\partial u}{\partial x_m}\frac{\partial u}{\partial x_k})^{\frac{p-2}{2}}a_{ij}(x)\frac{\partial u}{\partial x_j}]=\lambda g(x)|u|^{p-2}u + f(x,u,\lambda),u\in W_0^{1,p}(\Omega)\end{cases}$$ . We prove that the principal eigenvalue $\lambda_1$ of the eigenvalue problem $$\begin{cases}A_pu =\lambda g(x)|u|^{p-2}u,u\in W_0^{1,p}(\Omega),\end{cases}$$ is a bifurcation point of the problem mentioned above.