The existence and multiplicity of nontrivial solutions for a class of p-Monge-Ampère system - Ya-nan, Ma; Chenghua, Gao; Huanhuan, Ding (Topological Methods in Nonlinear Analysis, 2026)
In this paper, we deal with the following p-Monge-Ampère system:\begin{equation*}\begin{cases}\text{det}(D(|Du_{1}|^{p-2}Du_{1}))=f_{1}(|x|,-u_{2}), & x\in B,\\\text{det}(D(|Du_{2}|^{p-2}Du_{2}))=f_{2}(|x|,-u_{1}),& x\in B,\\u_{1}=u_{2}=0, & x\in\partial B,\end{cases}\end{equation*}where $B=\{x\in\mathbb{R}^{n}:|x|< 1\}$ and $f_{i}$ $(i=1,2)$ are continuous and nonnegative functions. Based on the fixed-point theory, some results regarding existence of radial solutions are established when $f_{i}$ $(i=1,2)$ satisfy some new growth conditions.