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

Author:

Wang Liangyu1,Li Hongyu1ORCID

Affiliation:

1. College of Mathematics and Systems Science, Shandong University of Science and Technology, Qingdao 266590, China

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.

Funder

National Natural Science Foundation of China

Shandong Natural Science Foundation

Publisher

MDPI AG

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