AN EXPLICIT FORMULA FOR THE SPLITTING OF MULTIPLE EIGENVALUES FOR NONLINEAR EIGENVALUE PROBLEMS AND CONNECTIONS WITH THE LINEARIZATION FOR THE DELAY EIGENVALUE PROBLEM

作者：Michiels Wim^*; Boussaada Islam; Niculescu Silviu Iulian

来源：SIAM Journal on Matrix Analysis and Applications, 2017, 38(2): 599-620.

DOI：10.1137/16M107774X

• nonlinear eigenvalue problems
• systems of functional equations and inequalities
• perturbations of nonlinear operators
• asymptotic distribution of eigenvalues and eigenfunctions
• matrix and operator equations

We contribute to the perturbation theory of nonlinear eigenvalue problems in three ways. First, we extend the formula for the sensitivity of a simple eigenvalue with respect to a variation of a parameter to the case of multiple nonsemisimple eigenvalues, thereby providing an explicit expression for the leading coefficients of the Puiseux series of the emanating branches of eigenvalues. Second, for a broad class of delay eigenvalue problems, the connection between the finitedimensional nonlinear eigenvalue problem and an associated infinite-dimensional linear eigenvalue problem is emphasized in the developed perturbation theory. Finally, in contrast to existing work on analyzing multiple eigenvalues of delay systems, we develop all theory in a matrix framework, i.e., without reduction of a problem to the analysis of a scalar characteristic quasi-polynomial.

• 出版日期2017