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In this paper, we study the existence and multiplicity of radially symmetric  k -admissible solutions for the  k -Hessian equation with 0-Dirichlet boundary condition{S  k    (    D  2   u   )   =  f   (   −  u   )in     B  ,u  =  0on     ∂  B  ,and the corresponding one-parameter problem, where  B  is a unit ball in ℝ  n   with  n  ≥ 1,  k  ∈ {1,…,  n },  f : [0, +∞) → [0, +∞) is continuous. We show that the  k -admissible solutions are not convex, so we construct a new cone and obtain the existence of triple and arbitrarily many  k -admissible solutions via the Leggett-Williams’ fixed point theorem.

Existence and Multiplicity of Radially Symmetric k -Admissible Solutions for Dirichlet Problem of k -Hessian Equations