发表机构
School of Mathematics and Statistics, Henan University（河南大学数学与统计学院）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文证明弱超调和条件使平坦常Q/R-曲率方程的正整解自动可容许，从而分类为正常数或标准气泡，并揭示该条件在结构上必要，移除后存在单参数族振荡解。
AI 中文摘要
我们研究维度$n\geq5$中平坦常$Q/R$-曲率方程的正整解。我们证明弱超调和条件$-\Delta u\geq0$已经迫使每个非常数解都是可容许的。凭借这种自动可容许性，我们将所有此类解分类为正常数或标准气泡。我们还表明弱超调和条件在结构上是必要的。一旦移除该条件，在每个正常数附近就存在一个单参数族的正径向整解。这些解在无穷远处收敛到一个正常数，而$-\Delta u$和$-\Delta(u^{(n-2)/(n-4)})$都无限多次变号。
英文摘要
We study positive entire solutions of the flat constant $Q/R$-curvature equation in dimension $n\geq5$. We prove that the weak superharmonicity condition $-Δu\geq0$ already forces every nonconstant solution to be admissible. With this automatic admissibility, we classify all such solutions as positive constants or standard bubbles. We also show that the weak superharmonicity condition is structurally necessary. Once it is removed, there is a one-parameter family of positive radial entire solutions near every positive constant. These solutions converge to a positive constant at infinity, while both $-Δu$ and $-Δ(u^{(n-2)/(n-4)})$ change sign infinitely many times.
