Bifurcation and nonnegative solutions for problem with mean curvature operator on general domain∗

We establish the existence/nonexistence and multiplicity of nontrivial nonnegative solutions for the following 0-Dirichlet problem with mean curvature operator in the Minkowski space  −div ( ∇u √ 1−|∇u|2 ) = λf(x, u) in Ω, u = 0 on ∂Ω, where Ω is a general bounded domain of RN . By bifurcation and topological methods, we determine the interval of parameter λ in which the above problem has zero/one/two nontrivial nonnegative solutions according to sublinear/linear/superlinear nonlinearity at zero. Moreover, we also amend a minor fault in [2, Proposition 1.1].