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Simple proofs of some results in perturbed bifurcation theory

Published online by Cambridge University Press:  14 November 2011

K. J. Brown  and
R. Shivaji
K. J. Brown
Affiliation:
Department of Mathematics, Heriot–Watt University, Riccarton, Currie, Edinburgh EH14 4AS
R. Shivaji
Affiliation:
Department of Mathematics, Heriot–Watt University, Riccarton, Currie, Edinburgh EH14 4AS
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Synopsis

In this paper we discuss the existence and multiplicity of solutions to some perturbed bifurcation problems. By using sub and supersolution techniques along with an anti-maximum principle, simple proofs of some “well known” local results of perturbed bifurcation theory are obtained. The existence of global continua of solutions is proved by using degree theory arguments.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 93 , Issue 1-2 , 1982 , pp. 71 - 82
Copyright
Copyright © Royal Society of Edinburgh 1982

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