The existence and multiplicity of nontrivial solutions for a class of p-Monge-Ampère system
DOI:
https://doi.org/10.12775/TMNA.2025.043Słowa kluczowe
p-Monge-Ampère equation, radial solutions, existence, multiplicity, fixed-point theoremAbstrakt
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.Bibliografia
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