Journal of Applied Mathematics and Stochastic Analysis 
Volume 5 (1992), Issue 1, Pages 1-17
doi:10.1155/S1048953392000017

On solvability of mixed monotone operator equations with applications to mixed quasimonotone differential systems involving discontinuities

S. Heikkilä,1 M. Kumpulainen,1 and V. Lakshmikantham2

 1University of Oulu, Department of Mathematics, Oulu 57 SF-90570, Finland
2Florida Institute of Technology, Department of Applied Mathematics, Melbourne 32901-6988, Florida, USA
Received 1 July 1991; Revised 1 September 1991

Abstract

In this paper we shall first study solvability of mixed monotone systems of operator equations in an ordered normed space by using a generalized iteration method. The obtained results are then applied to prove existence of coupled extremal quasisolutions of the systems of first and second order mixed quasimonotone differential equations with discontinuous right hand sides. Most of the results deal with systems in a Banach space ordered by a regular order cone.