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A Technic in Perturbation Theory

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A Technic in Perturbation Theory

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dc.contributor.author Ladde, G. S. en
dc.contributor.author Leela, S. en
dc.contributor.author Lakshmikantham, V. en
dc.date.accessioned 2010-05-25T18:03:35Z en
dc.date.available 2010-05-25T18:03:35Z en
dc.date.issued 1974-07 en
dc.identifier.uri http://hdl.handle.net/10106/2156 en
dc.description.abstract A study of the effect of perturbations of differential equations depends on the method employed and on the nature of perturbations. One of the most used technics is that of Lyapunov method and the other is the nonlinear variation of parameters formula [3]. These methods dictate that we measure the perturbations by means of a norm and thus destroy the ideal nature, if any, of the perturbing terms. Recently an effort was made to correct this unpleasant situation [1,2]. In this paper, we wish to develop a new comparison theorem that connects the solutions of perturbed and unperturbed differential systems in a manner useful in the theory of perturbations. This comparison result blends, in a sense, the two approaches mentioned earlier and consequently provides a flexible mechanism to preserve the nature of perturbations. Our results will show that the usual comparison theorem in terms of Lyapunov function is imbedded as a special case in our present theorem and that the perturbation theory could be studied in a more fruitful way. An example is worked out to illustrate the results. en
dc.language.iso en_US en
dc.publisher University of Texas at Arlington en
dc.relation.ispartofseries Technical Report;14 en
dc.subject Perturbations en
dc.subject Lyapunov method en
dc.subject Theory of perturbations en
dc.subject Lyapunov method en
dc.subject Nonlinear variation of parameters en
dc.subject Perturbations en
dc.subject.lcsh Perturbation (Mathematics) en
dc.subject.lcsh Mathematics Research en
dc.subject.lcsh Perturbation (Mathematics) en
dc.subject.lcsh Mathematics Research en
dc.title A Technic in Perturbation Theory en
dc.type Technical Report en
dc.publisher.department Department of Mathematics en

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