论文标题
在有限域中对关键椭圆系统的多个爆破解决方案
Multiple blowing-up solutions to critical elliptic systems in bounded domains
论文作者
论文摘要
我们在欧几里得空间的平滑界面域上为椭圆系统构建了吹式解决方案的家族，这些家族是关键车道填充系统的变体，并且类似于Brezis-Nirenberg问题。我们找到一个控制爆炸点和速率的功能，观察到它反映了系统的强非线性特征。通过使用它，我们还证明了在一般域中存在一个单一的爆破解决方案，并构建了允许存在多个吹式溶液的合同域的示例。我们认为，这里提出的各种新思想和论点将有助于分析相关的哈密顿型系统中的爆炸现象。
We construct families of blowing-up solutions to elliptic systems on smooth bounded domains in the Euclidean space, which are variants of the critical Lane-Emden system and analogous to the Brezis-Nirenberg problem. We find a function which governs blowing-up points and rates, observing that it reflects the strong nonlinear characteristic of the system. By using it, we also prove that a single blowing-up solution exists in general domains, and construct examples of contractible domains where multiple blowing-up solutions are allowed to exist. We believe that a variety of new ideas and arguments developed here will help to analyze blowing-up phenomena in related Hamiltonian-type systems.
