Geodesic
Stability of eigenvalues of some singular integral equations under compact perturbations
Zapiski Nauchnykh Seminarov POMI, Boundary-value problems of mathematical physics and related problems of function theory. Part 16, Tome 138 (1984), pp. 127-136

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We find some necessary and sufficient conditions on the symbol $s(A)$ of a singular integral operator $A$ (or a Wiener-Hopf operator, or an operator of a system of dual integral equations) for the equations $(A+C)f=\lambda f$ have notrivial solutions for every compact perturbation $C$. 
@article{ZNSL_1984_138_a8,
     author = {L. N. Nikol'skaya},
     title = {Stability of eigenvalues of some singular integral equations under compact perturbations},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {127--136},
     publisher = {mathdoc},
     volume = {138},
     year = {1984},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_1984_138_a8/}
}
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L. N. Nikol'skaya. Stability of eigenvalues of some singular integral equations under compact perturbations. Zapiski Nauchnykh Seminarov POMI, Boundary-value problems of mathematical physics and related problems of function theory. Part 16, Tome 138 (1984), pp. 127-136. http://geodesic.mathdoc.fr/item/ZNSL_1984_138_a8/