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Newton's diagram method for nonlinear equations with several small parameters

Published online by Cambridge University Press:  17 February 2009

Peter Aizengendler
Peter Aizengendler
Affiliation:
Professor Peter Aizengendler, late of Pscov University, Russia, died in November 2000. This paper, his last mathematical testament, is published with the kind consent of his son, Dr Mark Aizengendler, 11 Varram Way, West Lakes Shore, SA 5020; e-mail:[email protected].
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Abstract

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In this article, we generalise Newton's diagram method for finding small solutions ξ(λ) of equations f (ξ,λ) = 0 (0,0) = 0 with f analytic (see [1, 2, 4, 6]) to the case of a multi-dimensional function f, unknown variable ζ and small parameter λ. This method was briefly described in [1]. The method has many different applications and allows one to solve some inflexible problems. In particular, the method can be used in very difficult bifurcation problems, for example, for systems with small imperfections.

Type
Research Article
Information
The ANZIAM Journal , Volume 44 , Issue 2 , October 2002 , pp. 247 - 259
Copyright
Copyright © Australian Mathematical Society 2002

References

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