We study the vanishing discount problem for a nonlinear monotone system of Hamilton–Jacobi equations. This continues the first author’s investigation on the vanishing discount problem for a monotone system of Hamilton–Jacobi equations. As in part 1, we introduce by the convex duality Mather measures and their analogues for the system, which we call respectively Mather and Green–Poisson measures, and prove a convergence theorem for the vanishing discount problem. Moreover, we establish an existence result for the ergodic problem.

中文翻译：

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Hamilton–Jacobi方程单调系统的消失贴现问题：第2部分：非线性耦合

我们研究了Hamilton–Jacobi方程的非线性单调系统的消失贴现问题。这是第一作者继续研究汉密尔顿-雅各比方程单调系统的消失贴现问题的方法。与第1部分一样，我们通过凸对偶性Mather测度及其系统的类似物（分别称为Mather和Green-Poisson测度）来介绍，并证明了消失的贴现问题的收敛定理。此外，我们建立了遍历问题的存在结果。