Count of eigenvalues in the generalized eigenvalue problem

We study isolated and embedded eigenvalues in the generalized eigenvalue problem defined by two self-adjoint operators with a positive essential spectrum and a finite number of isolated eigenvalues. The generalized eigenvalue problem determines the spectral stability of nonlinear waves in infinite-dimensional Hamiltonian systems. The theory is based on Pontryagin’s invariant subspace theorem and extends beyond the scope of earlier papers of …