Some global results for nonlinear eigenvalue problems
TLDR
In this paper, the structure of the solution set for a large class of nonlinear eigenvalue problems in a Banach space is investigated, and the existence of continua, i.e., closed connected sets, of solutions of these equations is demonstrated.About:
This article is published in Journal of Functional Analysis.The article was published on 1971-06-01 and is currently open access. It has received 1749 citations till now. The article focuses on the topics: C0-semigroup & Nonlinear system.read more
Citations
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Journal ArticleDOI
Positive solutions of nonlinear elliptic equations involving critical sobolev exponents
Haim Brezis,Louis Nirenberg +1 more
TL;DR: In this article, the existence of a fonction u satisfaisant l'equation elliptique non lineaire is investigated, i.e., a domaine borne in R n avec n ≥ 3.
Journal ArticleDOI
Bifurcation from simple eigenvalues
TL;DR: In this article, a general version of the main problem of bifurcation theory, given p ϵ C, determine the structure of G−1{0} in some neighborhood of p.
Book
Introduction to Numerical Continuation Methods
Eugene L. Allgower,Kurt Georg +1 more
TL;DR: The Numerical Continuation Methods for Nonlinear Systems of Equations (NCME) as discussed by the authors is an excellent introduction to numerical continuuation methods for solving nonlinear systems of equations.
Journal ArticleDOI
Bifurcation, perturbation of simple eigenvalues, itand linearized stability
TL;DR: In this article, the eigenvalue of minimum modulus of the Frechet derivative of a nonlinear operator is estimated along a bifurcating curve of zeros of the operator.
References
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Book
Methods of Mathematical Physics
Richard Courant,David Hilbert +1 more
TL;DR: In this paper, the authors present an algebraic extension of LINEAR TRANSFORMATIONS and QUADRATIC FORMS, and apply it to EIGEN-VARIATIONS.
Journal ArticleDOI
Methods of Mathematical Physics
TL;DR: In this paper, the authors present an algebraic extension of LINEAR TRANSFORMATIONS and QUADRATIC FORMS, and apply it to EIGEN-VARIATIONS.
Book ChapterDOI
On elliptic partial differential equations
TL;DR: In this paper, a series of lectures on the theory of elliptic differential equations is presented, including the Hilbert space approach to the Dirichlet problem for strongly elliptic systems, and various inequalities.