On quadratic eigenvalue problems arising in stability of discrete vortices

We develop a count of unstable eigenvalues in a finite-dimensional quadratic eigenvalue problem arising in the context of stability of discrete vortices in a multi-dimensional discrete nonlinear Schrödinger equation [D.E. Pelinovsky, P.G. Kevrekidis, D.J. Frantzeskakis, Persistence and stability of discrete vortices in nonlinear Schrödinger lattices, Physica D 212 (2005) 20–53]. The count is based on the Pontryagin Invariant Subspace Theorem …