Bifurcation and Nonnegative Solutions for Problems 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(del u/root 1-|del u|(2)) = lambda f(x,u) in Omega, u = 0 on partial derivative Omega, where Omega is a general bounded domain of R-N. By bifurcation and topological methods, we determine the interval of parameter lambda 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].