Abstract In this article we establish the a priori bounds of the Toda systems with arbitrarily many singular sources associated to the simple Lie algebras of type D 4 and F 4 , extending the previous works of Lin et al. [27] , [20] , [24] for the A n , B n , C n and G 2 type Lie algebras. The problem of obtaining a priori estimates can be reduced to locating the local mass of blowup solutions. The key step is to calculate the local mass near each blowup points efficiently. A precise estimate on the total mass of entire solutions of Toda systems with many singular sources is an indispensable step in our argument.

中文翻译：

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D4 和 F4 Toda 系统的先验估计

摘要 在本文中，我们建立了 Toda 系统的先验界限，其中任意多个奇异源与类型 D 4 和 F 4 的简单李代数相关联，扩展了 Lin 等人以前的工作。[27] , [20] , [24] 为 A n , B n , C n 和 G 2 型李代数。获得先验估计的问题可以简化为定位爆破解的局部质量。关键步骤是有效地计算每个爆破点附近的局部质量。对具有许多单一来源的 Toda 系统的整个解的总质量进行精确估计是我们论证中不可或缺的一步。