
Contents
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5.1 Construction of the Fundamental Family 5.1 Construction of the Fundamental Family
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5.2 Nesting, Limit Cases, and Simplifying The Family of Cones 5.2 Nesting, Limit Cases, and Simplifying The Family of Cones
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5.3 The Fundamental Nature of the Family of Monotonicity Cones 5.3 The Fundamental Nature of the Family of Monotonicity Cones
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Five A Fundamental Family of Monotonicity Cone Subequations
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Published:October 2023
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Abstract
This chapter constructs a family of monotonicity cone subequations. This is fundamental in the sense that if a given subequation β± is π-monotone for a monotonicity subequation π, then there exists an element πβ of the fundamental family with πββπ. That is, the family provides a fundamental neighborhood system for π0 among all convex cone subequations. Note that πΜββπ implies πΜβπΜβ, so that if the zero maximum principle (ZMP) holds for πΜβ it will also hold for πΜ. In order to construct the fundamental family, the chapter uses intersections of five elementary monotonicity cone subequations to build up a family of seventeen distinct monotonicity cone subequations for use in the main comparison theorem of Chapter 7.
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