Approximation and convergence rate of nonlinear eigenvalues: Lipschitz perturbations of a bounded self-adjoint operator

DOI10.1016/j.jmaa.2017.06.070zbMath1439.47044OpenAlexW2732487148MaRDI QIDQ2014125

Raffaele Chiappinelli

Publication date: 10 August 2017

Published in: Journal of Mathematical Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jmaa.2017.06.070

zbMATH Keywords

bifurcation theorygradient operatornonlinear Rayleigh quotientasymptotics of nonlinear eigenvaluesgeometric multiplicity of an eigenvaluepersistent eigenvalues and eigenvectors

Mathematics Subject Classification ID

Sobolev spaces and other spaces of ``smooth functions, embedding theorems, trace theorems (46E35) Perturbation theory of linear operators (47A55) Linear operators on special spaces (weighted shifts, operators on sequence spaces, etc.) (47B37) Nonlinear spectral theory, nonlinear eigenvalue problems (47J10) Applications of operator theory to differential and integral equations (47N20)

Related Items

The Brouwer degree associated to classical eigenvalue problems and applications to nonlinear spectral theory, Global persistence of the unit eigenvectors of perturbed eigenvalue problems in Hilbert spaces, Global continuation in Euclidean spaces of the perturbed unit eigenvectors corresponding to a simple eigenvalue, Oscillatory bifurcation problems for ODEs with logarithmic nonlinearity, What do you mean by ``Nonlinear eigenvalue problems?, A degree associated to linear eigenvalue problems in Hilbert spaces and applications to nonlinear spectral theory

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Topological persistence of the unit eigenvectors of a perturbed Fredholm operator of index zero
• Topological persistence of the normalized eigenvectors of a perturbed self-adjoint operator
• Local structure of bifurcation curves for nonlinear Sturm-Liouville problems
• A-priori bounds and asymptotics on the eigenvalues in bifurcation problems for perturbed self-adjoint operators
• Precise spectral asymptotics for nonlinear Sturm-Liouville problems
• Numerical solution for the nonlinear eigenvalue problems in bifurcation points
• Bifurcation from simple eigenvalues
• PERSISTENCE OF THE NORMALIZED EIGENVECTORS OF A PERTURBED OPERATOR IN THE VARIATIONAL CASE
• NORMALIZED EIGENVECTORS OF A PERTURBED LINEAR OPERATOR VIA GENERAL BIFURCATION
• On nonlinear eigenvalue problems
• ASYMPTOTIC BIFURCATION RESULTS FOR QUASILINEAR ELLIPTIC OPERATORS
• Upper and lower bounds for eigenvalues of nonlinear elliptic equations: I. The lowest eigenvalue
• On the concept of orientability for Fredholm maps between real Banach manifolds