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
=
0
on
∂
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.
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