On Complete Convex Solutions of Equations Similar to the Improper Affine Sphere Equation - Kokarev, V. N. (Журнал математичної фізики, аналізу, геометрії, 2007)
Let σ_k – the sum of all k-order Hessian principal minors (z_ij) for the function z(x^1,…,x^n). If φ of the n-1 positive variable belongs to the C^3,α class, 0<α<1 and if it is sufficiently close to the identically single function, then any complete convex solution z(x^1,…,x^n) of the equation σ_n=φ(σ_1,…,σ_n-1) is a quadratic polynomial. Mathematics Subject Classification: 58J05.