In this paper we first prove a general result about the uniqueness and non-degeneracy of positive radial solutions to equations of the form \(\Delta u+g(u)=0\). Our result applies in particular to the double power non-linearity where \(g(u)=u^q-u^p-\mu u\) for \(p>q>1\) and \(\mu >0\), which we discuss with more details. In this case, the non-degeneracy of the unique solution \(u_\mu \) allows us to derive its behavior in the two limits \(\mu \rightarrow 0\) and \(\mu \rightarrow \mu _*\) where \(\mu _*\) is the threshold of existence. This gives the uniqueness of energy minimizers at fixed mass in certain regimes. We also make a conjecture about the variations of the \(L^2\) mass of \(u_\mu \) in terms of \(\mu \), which we illustrate with numerical simulations. If valid, this conjecture would imply the uniqueness of energy minimizers in all cases and also give some important information about the orbital stability of \(u_\mu \).

在本文中，我们首先证明关于形式为\（\ Delta u + g（u）= 0 \）的方程组的正向径向解的唯一性和非简并性的一般结果。我们的结果尤其适用于双动力非线性其中\（克（U）= U ^曲^对- \亩U \）为\（P> Q> 1 \）和\（\亩> 0 \），我们将对其进行详细讨论。在这种情况下，唯一解\（u_ \ mu \）的非简并性允许我们在两个极限\（\ mu \ rightarrow 0 \）和\（\ mu \ rightarrow \ mu _ * \ ）其中\（\ mu _ * \）是生存的门槛。这在某些情况下具有固定质量的能量最小化器的独特性。我们还做出关于的变化推测\（L ^ 2 \）的质量\（U_ \亩\）在以下方面\（\亩\） ，我们示出了具有数值模拟。如果有效，这种推测将暗示能量最小化器在所有情况下都是唯一的，并且还会提供有关\（u_ \ mu \）的轨道稳定性的一些重要信息。