Spectrum, bifurcation and hypersurfaces of prescribed k-th mean curvature in Minkowski space

By bifurcation and topological methods, we study the existence/nonexistence and multiplicity of one-sign or nodal solutions of the following k-th mean curvature problem in Minkowski spacetime......... rN- k v1- v2 k =. N Ck N rN-1Hk( r, v) in (0, R), | v| < 1 in (0, R), v (0) = v(R) = 0. As a previous step, we investigate the spectral structure of its linearized problem at zero. Moreover, we also obtain a priori bounds and the asymptotic behaviors of solutions with respect to..