On Solvability of Mixed Monotone Operator Equations with Applications to Mixed Quasimonotone Differential Systems Involving Discontinuities

Authors

Seppo V. Heikkilä
Martti Kumpulainen
V. Lakshmikantham

Document Type

Article

Publication Title

Journal of Applied Mathematics and Stochastic Analysis

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.

First Page

1

Last Page

17

DOI

10.1155/S1048953392000017

Publication Date

1992

Recommended Citation

S. Heikkilä, M. Kumpulainen, and V. Lakshmikantham, “On solvability of mixed monotone operator equations with applications to mixed quasimonotone differential systems involving discontinuities,” Journal of Applied Mathematics and Stochastic Analysis, vol. 5, no. 1, pp. 1-17, 1992. doi:10.1155/S1048953392000017