An Ambrosetti-Prodi-type problem for an elliptic system of equations via monotone iteration method and Leray-Schauder degree theory

Abstract

In this paper we employ the Monotone Iteration Method and the Leray-Schauder Degree Theory to study an ${ℝ}^2$-parametrized system of elliptic equations. We obtain a curve dividing the plane into two regions. Depending on which region the parameter is, the system will or will not have solutions. This is an Ambrosetti-Prodi-type problem for a system of equations.