Nodal Solutions for a Nonhomogeneous Elliptic Equation with Symmetry

We consider the semilinear problem $-\Delta u + \lambda u =|u|^{p-2}u + f(u)$ in $\Omega$, $u=0$ on $\partial \Omega$ where $\Omega \subset \mathbb{R}^N$ is a bounded smooth domain, $2