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Inverse-monotone nonlinear differential operators of the second order

Published online by Cambridge University Press:  14 November 2011

Johann Schröder
Johann Schröder
Affiliation:
Mathematisches Institut, Universität zu Köln
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Synopsis

This paper provides a survey on a class of methods to obtain sufficient conditions for the inversemonotonicity of second-order differential operators. Pointwise differential inequalities as well as weak differential inequalities are treated. In particular, the theory yields results on the relation between inverse-mo no tone operators and monotone definite operators, i.e. monotone operators in the Browder–Minty sense. This presentation is restricted to ordinary differential operators. Most methods explained here can also be applied to elliptic-parabolic partial differential operators in essentially the same way.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 79 , Issue 3-4 , 1978 , pp. 193 - 226
Copyright
Copyright © Royal Society of Edinburgh 1978

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