The infimum of the least eigenvalues of all finite induced subgraphs of an infinite graph is defined to be its least eigenvalue. In [P.J. Cameron, J.M. Goethals, J.J. Seidel and E.E. Shult, Line graphs, root systems, and elliptic geometry, J. Algebra 43 (1976) 305–327], the class of all finite graphs whose least eigenvalues > −2 has been classified: (1) If a (finite) graph is connected and its ...

In this paper the eigenvalue problem for a generalized hemivariational inequality is studied. Some general existence results are obtained. Applications from Engineering illustrate the theory.

This paper is concerned with the Hermitian definite generalized eigenvalue problem A− λB for block diagonal matrices A 1⁄4 diagðA11; A22Þ and B 1⁄4 diagðB11; B22Þ. Both A and B are Hermitian, and B is positive definite. Bounds on how its eigenvalues vary when A and B are perturbed by Hermitian matrices are established. These bounds are generally of linear order with respect to the perturbations...

Abstract It is well-known that the finite difference discretization of Laplacian eigenvalue problem ? ?u = ?u leads to a matrix (EVP) Ax ?x where A Toeplitz-plus-Hankel. Analytical solutions tridiagonal matrices with various boundary conditions are given in recent work Strang and MacNamara. We generalize results develop analytical certain generalized problems (GEVPs) ?Bx which arise from elemen...