Perturbations of embedded eigenvalues for self-adjoint ODE systems

• We consider a perturbation problem for embedded eigenvalues of a self-adjoint differential operator in L2(R;Rn). In particular, we study the set of all small perturbations in an appropriate Banach space for which the embedded eigenvalue remains embedded in the continuous spectrum. We show that this set of small perturbations forms a smooth manifold and we specify its co-dimension. Our methods involve the use of exponential dichotomies, their roughness property and Lyapunov-Schmidt reduction.

Subject headings

NATURVETENSKAP  -- Matematik -- Matematisk analys (hsv//swe)

NATURAL SCIENCES  -- Mathematics -- Mathematical Analysis (hsv//eng)

Publication and Content Type

art (subject category)

ref (subject category)