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SOLUTION BRANCHES OF NONLINEAR EIGENVALUE PROBLEMS ON RESTRICTED DOMAINS

Part of: Equations and inequalities involving nonlinear operators

Published online by Cambridge University Press:  13 March 2020

SHANE ARORA Open the ORCID record for SHANE ARORA [Opens in a new window]
SHANE ARORA*
Affiliation:
School of Mathematics and Statistics,University of Sydney, Camperdown, NSW2006, Australia email [email protected]
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Abstract

We extend bifurcation results of nonlinear eigenvalue problems from real Banach spaces to any neighbourhood of a given point. For points of odd multiplicity on these restricted domains, we establish that the component of solutions through the bifurcation point either is unbounded, admits an accumulation point on the boundary, or contains an even number of odd-multiplicity points. In the simple-multiplicity case, we show that branches of solutions in the directions of corresponding eigenvectors satisfy similar conditions on such restricted domains.

Keywords

nonlinear eigenvalue problembifurcation theorycompact operators

MSC classification

Primary: 47J10: Nonlinear spectral theory, nonlinear eigenvalue problems
Secondary: 47J15: Abstract bifurcation theory
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 102 , Issue 3 , December 2020 , pp. 490 - 497
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Copyright
© 2020 Australian Mathematical Publishing Association Inc.

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References

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