Nonlinear perturbations of a linear elliptic problem near its first eigenvalue
نویسندگان
چکیده
منابع مشابه
A linear eigenvalue algorithm for the nonlinear eigenvalue problem
The Arnoldi method for standard eigenvalue problems possesses several attractive properties making it robust, reliable and efficient for many problems. Our first important result is a characterization of a general nonlinear eigenvalue problem (NEP) as a standard but infinite dimensional eigenvalue problem involving an integration operator denoted B. In this paper we present a new algorithm equi...
متن کاملA Nonlinear Eigenvalue Problem
My lectures at the Minicorsi di Analisi Matematica at Padova in June 2000 are written up in these notes1. They are an updated and extended version of my lectures [37] at Jyväskylä in October 1994. In particular, an account of the exciting recent development of the asymptotic case is included, which is called the ∞-eigenvalue problem. I wish to thank the University of Padova for financial suppor...
متن کاملAn Eigenvalue Problem for Nonlinear Elliptic Partial Differential Equations
where X is a real number and/(i,x) is a real-valued function defined on R1 x G with /(0, x) s 0. If/(u,x) = u, the study of the boundary value problem (1) forms the foundation of the spectral analysis of A, a problem of great importance both in mathematics and its applications. If f(u,x) does not depend on « in a linear manner, one enters the relatively uncharted world of nonlinear functional a...
متن کاملSimplicity and stability of the first eigenvalue of a nonlinear elliptic system
Note that the system (1.1) is of two second-order elliptic equations. It is weakly coupled in the sense that interaction is present only in the “source terms,” while the differential terms have only one dependent variable. The differential operator involved is the so-called p-Laplacian, that is, ∆pu = ∇ · (|∇u|p−2∇u), which reduces to the ordinary Laplace operator ∆u when p = 2. We mention that...
متن کاملVariational Methods for Nonlinear Elliptic Eigenvalue Problems
In the present note, we give a simple general proof for the existence of solutions of the following two types of variational problems: PROBLEM A. To minimize fa F(x> u, • • • , Du)dx over a subspace VofW>*(tt). PROBLEM B. TO minimize ƒ« F(x, w, • • • , Du)dx for u in V with / a G(x, u, • • • , D^u)dx^c. The solution of the first problem yields a weak solution of a corresponding elliptic boundar...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of Differential Equations
سال: 1978
ISSN: 0022-0396
DOI: 10.1016/0022-0396(78)90019-0