Variational methods for NLEV approximation near a bifurcation point
type: Item
instance of: scholarly article
title: Variational methods for NLEV approximation near a bifurcation point
zbMATH Open document ID: 1391.35303
DOI: 10.1155/2012/102489
author: Raffaele Chiappinelli
published in: International Journal of Mathematics and Mathematical Sciences
publication date: 2012-12-18T00:00:00Z
review text: Summary: 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 \(\mathbb R^N\). A section reviewing some general facts about eigenvalues of linear and nonlinear operators is included.
Mathematics Subject Classification ID: 35P30
Mathematics Subject Classification ID: 35J60
zbMATH DE Number: 6116533
zbMATH Keywords: gradient operators
zbMATH Keywords: nonlinear eigenvalues
zbMATH Keywords: Lyapunov-Schmidt reduction
zbMATH Keywords: finite-dimensional kernel
zbMATH Keywords: semilinear elliptic operators
Wikidata QID: Q58705497
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2012/102489
OpenAlex ID: W2121386524
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description: scientific article; zbMATH DE number 6116533