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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 

 

A comparison principle for terminal value problems in ordinary differential equations


Author: Thomas G. Hallam
Journal: Trans. Amer. Math. Soc. 169 (1972), 49-57
MSC: Primary 34C10
DOI: https://doi.org/10.1090/S0002-9947-1972-0306611-3
MathSciNet review: 0306611
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Abstract: A comparison principle for a terminal value problem of an ordinary differential equation is formulated. Basic related topics such as the existence of maximal and minimal solutions of terminal value problems are investigated. The close relationship between the existence of the extremal solutions of a terminal value problem and the concept of asymptotic equilibrium of the differential equation is explored. Several applications of the terminal comparison principle are given.


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DOI: https://doi.org/10.1090/S0002-9947-1972-0306611-3
Keywords: Comparison principle, differential inequality, maximal and minimal solutions, terminal value problem, asymptotic equilibrium
Article copyright: © Copyright 1972 American Mathematical Society