We use Perron method to prove the existence of ancient solutions of exterior problem for a kind of parabolic Monge–Ampère equation \(-\,u_t\det D^2u=f\) with prescribed asymptotic behavior at infinity outside some certain bowl-shaped domain in the lower half space for \(n\ge 3\), where f is a perturbation of 1 at infinity. We raise this problem for the first time and construct a new subsolution to it. We also use similar method to prove the existence of the entire solutions.

中文翻译：

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抛物线 Monge-Ampère 方程外问题的古解

我们使用 Perron 方法证明了一种抛物线 Monge-Ampère 方程\(-\,u_t\det D^2u=f\)外问题的古解的存在性，该方程在某个碗形外具有规定的无穷远渐近行为\(n\ge 3\)的下半空间中的域，其中f是无穷远处的 1 扰动。我们第一次提出这个问题，并为它构建了一个新的子解决方案。我们也用类似的方法来证明整个解的存在性。