Bifurcation and admissible solutions for the Hessian equation

We study the following eigenvalue problem of k-Hessian equation{Sk(D2u)=λkf(−u)inB,u=0on∂B. Global bifurcation result is established for this problem. As applications of the bifurcation result, we determine the intervals of λ for the existence, nonexistence, uniqueness and multiplicity of radially symmetric k-admissible solutions for this problem.