In this note, we prove the Payne-type conjecture about the behaviour of the nodal set of least energy sign-changing solutions for the equation in bounded Steiner symmetric domains under the zero Dirichlet boundary conditions. The nonlinearity f is assumed to be either superlinear or resonant. In the latter case, least energy sign-changing solutions are second eigenfunctions of the zero Dirichlet p-Laplacian in ω. We show that the nodal set of any least energy sign-changing solution intersects the boundary of ω. The proof is based on a moving polarization argument.