Dirichlet problems with mean curvature operator in Minkowski space

摘要

We survey some existence and multiplicity results for Dirichlet problems with mean curvature operator in Minkowski space. We deal with positive radial solutions when the problem has radial symmetry, as well as nontrivial constant sign solutions for problems in general bounded domains. Discontinuous Dirichet problems are also considered. Our approaches combine variational techniques, lower and upper solutions method and topological degree arguments.