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Variational Methods for NLEV Approximation Near a Bifurcation Point
Author
Source
International Journal of Mathematics and Mathematical Sciences
Issue
Vol. 2012, Issue 2012 (31 Dec. 2012), pp.1-32, 32 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2012-11-13
Country of Publication
Egypt
No. of Pages
32
Main Subjects
Abstract EN
We review some more and less recent results concerning bounds on nonlinear eigenvalues (NLEV) for gradient operators.
In particular, we discuss the asymptotic behaviour of NLEV (as the norm of the eigenvector tends to zero) in bifurcation problems from the line of trivial solutions, considering perturbations of linear self-adjoint operators in a Hilbert space.
The proofs are based on the Lusternik-Schnirelmann theory of critical points on one side and on the Lyapounov-Schmidt reduction to the relevant finite-dimensional kernel on the other side.
The results are applied to some semilinear elliptic operators in bounded domains of ℝN.
A section reviewing some general facts about eigenvalues of linear and nonlinear operators is included.
American Psychological Association (APA)
Chiappinelli, Raffaele. 2012. Variational Methods for NLEV Approximation Near a Bifurcation Point. International Journal of Mathematics and Mathematical Sciences،Vol. 2012, no. 2012, pp.1-32.
https://search.emarefa.net/detail/BIM-446473
Modern Language Association (MLA)
Chiappinelli, Raffaele. Variational Methods for NLEV Approximation Near a Bifurcation Point. International Journal of Mathematics and Mathematical Sciences No. 2012 (2012), pp.1-32.
https://search.emarefa.net/detail/BIM-446473
American Medical Association (AMA)
Chiappinelli, Raffaele. Variational Methods for NLEV Approximation Near a Bifurcation Point. International Journal of Mathematics and Mathematical Sciences. 2012. Vol. 2012, no. 2012, pp.1-32.
https://search.emarefa.net/detail/BIM-446473
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-446473