On the absorption of eigenvalues by continuous spectrum in regular perturbation problems

We consider the family of operators A + λB with A and B self-adjoint and B relatively form bounded. We consider situations where as λ ↓ λ₁, some eigenvalue μ(λ) approaches the continuous spectrum of A + λB. Typical of our results is the following. If B is relatively form compact, and μ(λ) → μ(λ₁), then either $\text{(μ(λ) ? μ(λ}{}_1\text{))}\text{λ}\text{? λ}{}_1\text{→ 0}\text{or}\text{μ(λ}{}_1\text{)}$ is an eigenvalue of A + λ₁B.