We establish uniqueness of vanishing radially decreasing entire solutions, which we call ground states, to some semilinear fractional elliptic equations. In particular, we treat the fractional plasma equation and the supercritical power nonlinearity. As an application, we deduce uniqueness of radial steady states for nonlocal aggregation-diffusion equations of Keller-Segel type, even in the regime that is dominated by aggregation.

中文翻译：

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分数等离子问题的整个基态的唯一性

对于某些半线性分数椭圆方程，我们建立了消失的径向递减的整体解决方案（称为基态）的唯一性。特别地，我们处理分数阶等离子体方程和超临界功率非线性。作为一种应用，我们推论了Keller-Segel型非局部聚集-扩散方程的径向稳态唯一性，即使在以聚集为主导的状态下也是如此。