经典的打靶法是寻找一个合适的初始射击位置为了击中想要的目标。

这里制定的新方法，伴随着”目标图”核心的介绍和分析，自然而然的将古典的打靶法连接到简单而美丽的拓扑学理论。

我们应用新的方法，一个激励的例子，为了推导Hardy-Littlewood-Sobolev类型系统的全局正解： in in ，p，q0 在临界和超临界情况下 这里我们得到了证明对于拓扑度理论是否在一个合适的目标的估计。

这个和其他一些问题在这篇文章中完全解决了一些长期存在的开放问题和存不存在正整数解。

我们建立了正解的不存在的Hardy Littlewood Sobolev非线性方程的类型系统和相应的非线性微分系统的Lane-Emden方程。

这些不存在的结果，称为Liouville型定理，是基本的偏微分方程的理论与应用。

一个特殊的迭代格式，新的拍摄方法和一些Pohozaev型恒等式中的积分形式和微分形式的创造。

结合这些新技术的一些观察和一些关键的渐近分析，我们建立我们的非线性方程组的Liouville型锋利的标准。

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