### Nonlinear boundary value problems involving the extrinsic mean curvature operator

The paper surveys recent results obtained for the existence and multiplicity of radial solutions of Dirichlet problems of the type $$\nabla \xb7\left(\frac{\nabla v}{\sqrt{1-{\left|\nabla v\right|}^{2}}}\right)=f\left(\right|x|,v)\phantom{\rule{1.0em}{0ex}}\text{in}\phantom{\rule{4pt}{0ex}}{B}_{R},\phantom{\rule{1.0em}{0ex}}u=0\phantom{\rule{1.0em}{0ex}}\text{on}\phantom{\rule{4pt}{0ex}}\partial {B}_{R},$$ where ${B}_{R}$ is the open ball of center $0$ and radius $R$ in ${\mathbb{R}}^{n}$, and $f$ is continuous. Comparison is made with similar results for the Laplacian. Topological and variational methods are used and the case of positive solutions is emphasized. The paper ends with the case of a general domain.