Manifold method in the eigenvector theory of nonlinear operators. Transl. from the Russian

DOI10.1007/s10958-008-9200-6zbMath1152.35083OpenAlexW2020049396MaRDI QIDQ2518387

Yakov Mihajlovich Dymarskii

Publication date: 16 January 2009

Published in: Journal of Mathematical Sciences (New York) (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10958-008-9200-6

Mathematics Subject Classification ID

Nonlinear eigenvalue problems and nonlinear spectral theory for PDEs (35P30) Nonlinear spectral theory, nonlinear eigenvalue problems (47J10) Variational problems in infinite-dimensional spaces (58E99) Research exposition (monographs, survey articles) pertaining to partial differential equations (35-02) Ordinary differential operators (34L99)

Related Items (4)

Lax Equation on the Uhlenbeck Manifold ⋮ A quasilinear method in the theory of small eigenfunctions for nonlinear periodic boundary-value problems ⋮ Submanifolds of compact operators with fixed multiplicities of eigenvalues ⋮ On parametrization of the submanifold of matrices with a fixed structure of Jordan blocks

Cites Work

• The spectrum of the Laplacian and boundary perturbation. I
• On the number of unbounded solution branches in a neighborhood of an asymptotic bifurcation point
• A comparison of different spectra for nonlinear operators
• On the second eigenvalue of the Dirichlet Laplacian
• On the persistence of the multiplicity of eigenvalues for some variational elliptic operator depending on the domain
• Eigenfunctions for a class of nonlinear differential equations
• An eigenvalue theorem for nonlinear second-order differential equations
• Some global results for nonlinear eigenvalue problems
• Bifurcation from simple eigenvalues
• Modes and quasimodes
• Some spectral theory for nonlinear operators
• Bifurcation from higher eigenvalues in nonlinear elliptic equations: Continua that meet infinity
• The Choquard equation and related questions
• Orientation and the Leray-Schauder theory for fully nonlinear elliptic boundary value problems
• Bifurcation theory for Fredholm operators
• Generic Properties of Eigenfunctions
• NON-LINEAR FREDHOLM MAPS AND THE LERAY-SCHAUDER THEORY
• Structure of the spectrum of the Schrodinger operator with magnetic field in a strip and infinite-gap potentials
• An Infinite Dimensional Version of Sard's Theorem
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