We study radial sign-changing solutions of a class of fully nonlinear elliptic Dirichlet problems in a ball, driven by the extremal Pucci's operators and with a power nonlinear term. We first determine a new critical exponent related to the existence or nonexistence of such solutions. Then we analyze the asymptotic behavior of the radial nodal solutions as the exponents approach the critical values, showing that new concentration phenomena occur. Finally we define a suitable weighted energy for these solutions and compute its limit value.

中文翻译：

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一类径向完全非线性方程的新集中现象

我们研究球中一类完全非线性椭圆Dirichlet问题的径向符号转换解，该问题由极值Pucci算符驱动并且具有幂非线性项。我们首先确定与此类解决方案的存在或不存在相关的新的临界指数。然后，当指数接近临界值时，我们分析了径向节点解的渐近行为，表明出现了新的集中现象。最后，我们为这些解决方案定义合适的加权能量，并计算其极限值。