Abstract and Applied Analysis
Volume 1 (1996), Issue 2, Pages 137-152

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

D. C. de Morais Filho

Departamento de Matemática e Estatística, Universidade Federal da Paraíba, Caixa Postal 10044, Campina Grande 58.109-970, Pb, Brazil

Received 7 March 1996

Copyright © 1996 D. C. de Morais Filho. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


In this paper we employ the Monotone Iteration Method and the Leray-Schauder Degree Theory to study an 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.