In this paper, we focus on the following coupled system of $k$-Hessian equations:
$\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \begin{equation*} \left\{\begin{aligned}&S_k(\lambda(D^2u))=f_1(|x|,-v)\ \ \ \ \ \ \ \ {\rm in}\ B,\\&S_k(\lambda(D^2v))=f_2(|x|,-u)\ \ \ \ \ \ \ \ {\rm in}\ B,\\&u=v=0 \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ {\rm on}\ \partial B.\end{aligned}\right.\end{equation*}$
Here B is a unit ball with center 0 and $f_i (i=1,2)$ are continuous and nonnegative functions. By introducing some new growth conditions on the nonlinearities $f_1$ and $f_2$, which are more flexible than the existing conditions for the k-Hessian systems (equations), several new existence and multiplicity results for k-convex solutions for this kind of problem are obtained.
Chenghua GAO
,
Xingyue HE
,
Jingjing WANG
. THE EXISTENCE AND MULTIPLICITY OF k-CONVEX SOLUTIONS FOR A COUPLED k-HESSIAN SYSTEM*[J]. Acta mathematica scientia, Series B, 2023
, 43(6)
: 2615
-2628
.
DOI: 10.1007/s10473-023-0618-1
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