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Lyapunov-like Vector Functions Using Pointwise Degenerate Systems as Comparison Functions

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Lyapunov-like Vector Functions Using Pointwise Degenerate Systems as Comparison Functions

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dc.contributor.author Asner, Bernard A., Jr. en
dc.contributor.author Lakshmikantham, V. en
dc.date.accessioned 2010-05-26T15:50:52Z en
dc.date.available 2010-05-26T15:50:52Z en
dc.date.issued 1974-04 en
dc.identifier.uri http://hdl.handle.net/10106/2176 en
dc.description.abstract The use of Lyapunov-like vector functions is recognized as an important tool for estimating the behavior of a dynamical system. In applications, one needs to determine a suitable comparison function which contains information or properties that can be used to obtain some information about the behavior of the dynamical system. In recent years, the remarkable property of pointwise degeneracy has been discovered for linear, autonomous, delay-differential equations. For this class of equations one knows that all solutions will reach a subspace in finite time and remain on the subspace thereafter. As this class of equations is particularly simple, it becomes an obvious candidate for use as a comparison function. In this paper (Section 3), we show how one may effectively use pointwise degenerate systems as comparison functions. Section 4 treats functional differential equations which possess certain monotonic features. These monotonic properties do not appear to allow us to select pointwise degenerate systems as natural comparison functions. en
dc.language.iso en_US en
dc.publisher University of Texas at Arlington en
dc.relation.ispartofseries Technical Report;9 en
dc.subject Lyapunov-like functions en
dc.subject Pointwise degeneracy en
dc.subject Comparison functions en
dc.subject Differential equations en
dc.subject.lcsh Mathematics Research en
dc.title Lyapunov-like Vector Functions Using Pointwise Degenerate Systems as Comparison Functions en
dc.type Technical Report en
dc.publisher.department Department of Mathematics en

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