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An Intermediate Value Property for Operators with Applications to Integral and Differential Equations

Published online by Cambridge University Press:  20 November 2018

J. S. Muldowney  and
D. Willett
J. S. Muldowney
Affiliation:
University of Alberta, Edmonton, Alberta
D. Willett
Affiliation:
University of Alberta, Edmonton, Alberta
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It is well known that a real valued continuous function f on a closed interval S assumes every value between its maximum and minimum on S, i.e. if ξ is such that f(α) ≦ ξ ≦ f(β) then there exists γ between α and β such that f(γ) = ξ. The purpose of this paper is to develop the existence theory associated with differential and integral inequalities in the context of an intermediate value property for operators on partially ordered spaces. This has the advantage of allowing rather simple proofs of known results while in most cases giving slight improvements, and in some cases substantial improvements, in these results. Classical and recent results from different areas are unified under one principle.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 26 , Issue 1 , February 1974 , pp. 27 - 41
Copyright
Copyright © Canadian Mathematical Society 1974

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