TY - JOUR
AU - Coelho, Isabel
AU - Corsato, Chiara
AU - Rivetti, Sabrina
PY - 2016/04/12
Y2 - 2023/02/04
TI - Positive radial solutions of the Dirichlet problem for the Minkowski-curvature equation in a ball
JF - Topological Methods in Nonlinear Analysis
JA - TMNA
VL - 44
IS - 1
SE -
DO -
UR - https://apcz.umk.pl/TMNA/article/view/TMNA.2014.034
SP - 23 - 39
AB - We study the existence and multiplicity of positive radial solutions of the Dirichlet problem for the Minkowski-curvature equation$$\cases\displaystyle-\text{\rm div}\bigg( \frac{
abla v} {\sqrt{1 - |
abla v|^2}}\bigg)= f(|x|,v) &\quad \text{in } B_R,\\\displaystylev=0 & \quad \text{on } \partial B_R,\endcases$$< p> where $B_R$ is a ball in $\mathbb{R}^N$ ($N\ge 2$).According to the behaviour of $f=f(r,s)$ near $s=0$, we prove the existence of either one, two or three positive solutions.All results are obtained by reduction to an equivalent non-singular one-dimensional problem, to which variational methods can be applied in a standard way.
ER -