Variational Methods for NLEV Approximation Near a Bifurcation Point

Variational Methods for NLEV Approximation Near a Bifurcation Point

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 pert...

Full description

Bibliographic Details
Main Author: Raffaele Chiappinelli
Format: Article
Language:English
Published: Hindawi Limited 2012-01-01
Series:International Journal of Mathematics and Mathematical Sciences
Online Access:http://dx.doi.org/10.1155/2012/102489
id doaj-77f5dab80c0b456caba7c309c2807390
record_format Article
spelling doaj-77f5dab80c0b456caba7c309c28073902020-11-24T22:22:15ZengHindawi LimitedInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04252012-01-01201210.1155/2012/102489102489Variational Methods for NLEV Approximation Near a Bifurcation PointRaffaele Chiappinelli0Dipartimento di Scienze Matematiche ed Informatiche, Università di Siena, Pian dei Mantellini 44, 53100 Siena, ItalyWe 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 . A section reviewing some general facts about eigenvalues of linear and nonlinear operators is included.http://dx.doi.org/10.1155/2012/102489
collection DOAJ
language English
format Article
sources DOAJ
author Raffaele Chiappinelli
spellingShingle Raffaele Chiappinelli
Variational Methods for NLEV Approximation Near a Bifurcation Point
International Journal of Mathematics and Mathematical Sciences
author_facet Raffaele Chiappinelli
author_sort Raffaele Chiappinelli
title Variational Methods for NLEV Approximation Near a Bifurcation Point
title_short Variational Methods for NLEV Approximation Near a Bifurcation Point
title_full Variational Methods for NLEV Approximation Near a Bifurcation Point
title_fullStr Variational Methods for NLEV Approximation Near a Bifurcation Point
title_full_unstemmed Variational Methods for NLEV Approximation Near a Bifurcation Point
title_sort variational methods for nlev approximation near a bifurcation point
publisher Hindawi Limited
series International Journal of Mathematics and Mathematical Sciences
issn 0161-1712
1687-0425
publishDate 2012-01-01
description 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 . A section reviewing some general facts about eigenvalues of linear and nonlinear operators is included.
url http://dx.doi.org/10.1155/2012/102489
work_keys_str_mv AT raffaelechiappinelli variationalmethodsfornlevapproximationnearabifurcationpoint
_version_ 1725769180844654592

Similar Items