论文标题
非线性椭圆系统涉及Hardy-Sobolev关键性
Nonlinear elliptic systems involving Hardy-Sobolev Criticalities
论文作者
论文摘要
本文的重点是在$ \ mathbb {r}^n $中定义的非线性椭圆系统家族的溶解度。这样的方程式包含强大的电位和耐硬 - 核心的临界点，结合了可能的临界耐力性术语。该问题是作为毛 - 皮塔夫斯基（Pitaevskii）和玻色网型系统的概括而产生的。通过变异技术，我们将根据耦合参数$ν$以及不同参数和指数的顺序找到地面和绑定状态。特别是，对于广泛的参数，我们发现解决方案是在基础尼哈里歧管上的能量功能的最小化或山通临界点。
This paper is focused on the solvability of a family of nonlinear elliptic systems defined in $\mathbb{R}^N$. Such equations contain Hardy potentials and Hardy-Sobolev criticalities coupled by a possible critical Hardy-Sobolev term. That problem arises as a generalization of Gross-Pitaevskii and Bose-Einstein type systems. By means of variational techniques, we shall find ground and bound states in terms of the coupling parameter $ν$ and the order of the different parameters and exponents. In particular, for a wide range of parameters we find solutions as minimizers or Mountain-Pass critical points of the energy functional on the underlying Nehari manifold.
