Existence of multiple radial solutions for nonlinear equation involving the mean curvature operator in Lorentz-Minkowski space

Abstract

We prove existence of multiple radial solutions to the Dirichlet problem for nonlinear equations involving the mean curvature operator in Lorentz-Minkowski space and a nonlinear term of concave-convex type. Solutions are found using Szulkin's critical point theory for non-smooth functional. Multiplicity results are also given for some cases in which the nonlinearity depends also on the gradient of the solution.