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 $\textrm{div} \, \left( \frac{\nabla u}{\sqrt{1-| \nabla u |^2}}\right) + λq(| x |) | u |^{p-1} u = 0, \qquad u|_{\partial \mathcal{B}} = 0,$ where $\mathcal{B} \subset \mathbb{R}^N$ is a ball and $p > 1$, has more and more pairs of nodal solutions on growing of the parameter $λ> 0$. The radial Neumann problem and the periodic problem for the corresponding one-dimensional equation are considered, as well.

No reviews yet.

No comments yet.