On solvability of mixed monotone operator equations with applications to mixed quasimonotone differential systems involving discontinuities. (1992)

• Record Type: Journal Article
• Authors: Heikkilä, S.; Kumpulainen, M.; Lakshmikantham, V.
• Is Part Of: Journal of applied mathematics and stochastic analysis. Volume 5:Number 1(1992)
• Page Start: 1
• Page End: 17
• Publication Date: 1992
• Subjects: operator equations -- systems of differential equations in ordered Banach spaces -- discontinuous nonlinearity -- mixed quasimonotonicity -- generalized iteration method; Mathematical models -- Periodicals; Computer simulation -- Periodicals; Computer science -- Mathematics -- Periodicals; Computer science -- Mathematics; Computer simulation; Mathematical models; Applied Mathematics; Periodicals; Electronic journals; 519.22
• DOI: 10.1155/S1048953392000017
• Languages: English
• ISSNs: 1048-9533

Abstract

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.