Global Analysis of Two-Parameter Elliptic Eigenvalue Problems
نویسندگان
چکیده
منابع مشابه
Superconvergent Two-Grid Methods for Elliptic Eigenvalue Problems
Some numerical algorithms for elliptic eigenvalue problems are proposed, analyzed, and numerically tested. The methods combine advantages of the two-grid algorithm (Xu and Zhou in Math Comput 70(233):17–25, 2001), the two-space method (Racheva and Andreev in ComputMethods ApplMath 2:171–185, 2002), the shifted inverse powermethod (Hu and Cheng in Math Comput 80:1287–1301, 2011; Yang and Bi in S...
متن کاملPrediction of critical boundaries in two-parameter nonlinear eigenvalue problems
Prediction of critical boundaries (i.e. curves of singular points) in two-parameter nonlinear eigenvalue problems is considered. A generalization of the Krylov subspace for the one-parameter linear eigenvalue problem to the two-parameter case, suitable for the prediction of critical boundaries, is introduced. Methods for the eecient computation of the solution surface are developed. A case of t...
متن کاملJacobi-Davidson methods for polynomial two-parameter eigenvalue problems
We propose Jacobi–Davidson type methods for polynomial two-parameter eigenvalue problems (PMEP). Such problems can be linearized as singular two-parameter eigenvalue problems, whose matrices are of dimension k(k + 1)n/2, where k is the degree of the polynomial and n is the size of the matrix coefficients in the PMEP. When k2n is relatively small, the problem can be solved numerically by computi...
متن کاملOrlicz Spaces and Nonlinear Elliptic Eigenvalue Problems
Nonlinear elliptic differential equations of order m acting in a space of m dimensions often occupy a special position in more general theories. In this paper we shall study one aspect of this situation. The nonlinear problem under consideration will be the variational approach to eigenvalue problems for nonlinear elliptic partial differential equations as developed by the author in [l], [2], [...
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: Transactions of the American Mathematical Society
سال: 1984
ISSN: 0002-9947
DOI: 10.2307/1999990