Affiliation:
1. School of Applied Science, Beijing Information Science & Technology University , Beijing , 100192 , PR China
2. School of Mathematics and Physics, North China Electric Power University , Beijing , 102206 , PR China
Abstract
Abstract
The primary objective of this article is to analyze the existence of infinitely many radial
p
p
-
k
k
-convex solutions to the boundary blow-up
p
p
-
k
k
-Hessian problem
σ
k
(
λ
(
D
i
(
∣
D
u
∣
p
−
2
D
j
u
)
)
)
=
H
(
∣
x
∣
)
f
(
u
)
in
Ω
,
u
=
+
∞
on
∂
Ω
.
{\sigma }_{k}\left(\lambda \left({D}_{i}\left({| Du| }^{p-2}{D}_{j}u)))=H\left(| x| )f\left(u)\hspace{0.33em}\hspace{0.1em}\text{in}\hspace{0.1em}\hspace{0.33em}\Omega ,\hspace{0.33em}u=+\infty \hspace{0.33em}\hspace{0.1em}\text{on}\hspace{0.1em}\hspace{0.33em}\partial \Omega .
Here,
k
∈
{
1
,
2
,
…
,
N
}
k\in \left\{1,2,\ldots ,N\right\}
,
σ
k
(
λ
)
{\sigma }_{k}\left(\lambda )
is the
k
k
-Hessian operator, and
Ω
\Omega
is a ball in
R
N
(
N
≥
2
)
{{\mathbb{R}}}^{N}\hspace{0.33em}\left(N\ge 2)
. Our methods are mainly based on the sub- and super-solutions method.
Subject
General Mathematics,Statistical and Nonlinear Physics
Cited by
7 articles.
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