The Monge–Ampère equation with infinite boundary value

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Hessian equations with Infinite Dirichlet Boundary Value (2006, background): “7 in [7], one has a strictly convex radially symmetric positive function ũ ∈ C∞(R) satisfying (3.”
Boundary behavior of large solutions to the Monge-Ampère equations with weights (2015, result): “2 in [18], Theorem 3.”
On the Monge–Ampère equation with boundary blow-up: existence, uniqueness and asymptotics (2007, methodology): “The Monge– Ampère equation with boundary blow-up has been treated in [23,29] and [19], while the more general case of Hessian equations has been studied in [34] and [14].”
On the existence of solutions to the Monge-Ampère equation with infinite boundary values (2006, background): “In this case we note that φ′ 0 and that φ(s) → ∞ as s → 0+. Direct computation shows that (−φ′)n+1 = F (φ) and (n + 1)(−φ)n−1φ′′ = f(φ).”