Existence of eigenvalues of operators acting in $L^2(R^n)$

We write out conditions that help to prove the existence of eigenvalues and characteristic values for operator $F(D)-C(\lambda): L^{2}(R^{m})\to L^{2}(R^{m})$, where $F(D)$ is a pseudodifferential operator with a symbol $F(i\xi)$ and $C(\lambda): L^{2}(R^{m}) \to L^{2}(R^{m})$ is a linear continuous operator.