Solvability Criterion for a System Arising from Monge–Ampère Equations with Two Parameters

Abstract

Monge–Ampère equations have important research significance in many fields such as geometry, convex geometry and mathematical physics. In this paper, under some superlinear and sublinear conditions, the existence of nontrivial solutions for a system arising from Monge–Ampère equations with two parameters is investigated based on the Guo–Krasnosel’skii fixed point theorem. In the end, two examples are given to illustrate our theoretical results.