Pairs of nodal solutions for a Minkowski-curvature boundary value problem in a ball

By using a shooting technique, we prove that the quasilinear boundary value problem $$\text{div}\left(\frac{\mathrm{\nabla }u}{\sqrt{1-\mathrm{\mid }\mathrm{\nabla }u{\mathrm{\mid }}^2}}\right)+\lambda q(\mathrm{\mid }x\mathrm{\mid })\mathrm{\mid }u{\mathrm{\mid }}^{p-1}u=0,u{\mathrm{\mid }}_{\mathrm{\partial }\mathcal{B}}=0,$$ where $\mathcal{B}\subset {\mathbb{R}}^N$ is a ball and $p > 1$,hasmoreandmorepairsofnodalsolutionsongrowingoftheparameter$\lambda > 0$. The radial Neumann problem and the periodic problem for the corresponding one-dimensional equation are considered, as well.