Necessary and sufficient conditions of entire subsolutions to Monge–Ampère type equations
Tóm tắt
The primary objective of this article is to investigate the Monge–Ampère type equation
$$\text {det}^{\frac{1}{n}}(D^2u+A(x,u,Du))=f(u)$$
in
$${\mathbb {R}}^n$$
. Among others, the necessary and sufficient condition on f for the existence of entire subsolutions is established. This is probably the first time the necessary and sufficient conditions for the existence of entire subsolutions of Monge–Ampère type equations with A depending on Du has been studied.
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