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

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