Radial Convex Solutions of Boundary Value Problems for Systems of Monge-Ampere equations

TL;DR

This paper investigates the existence and multiplicity of radial convex solutions for a system of coupled Monge-Ampere equations using fixed point theory, providing conditions for when solutions exist or do not.

Contribution

It establishes new criteria for the existence, multiplicity, and nonexistence of solutions to coupled Monge-Ampere systems under asymptotic conditions, employing Krasnoselskii's fixed point theorem.

Findings

Conditions for existence of solutions are identified.

Criteria for nonexistence of solutions are provided.

Multiple solutions can be obtained under certain parameters.

Abstract

The existence, multiplicity and nonexistence of nontrivial radial convex solutions of a system of two weakly coupled Monge-Ampere equations are established with asymptotic assumptions for an appropriately chosen parameter. The proof of the results is based on Krasnoselskii's fixed point theorem in a cone.