M. Langer,
Eigenvalues of a λ-rational Sturm–Liouville problem,
Math. Nachr. 210 (2000), 163–176

Abstract:
The Sturm–Liouville problem

y'' + (λ + q/(u – λ))y = 0,
y(0) = 0,   y(1) = 0,
is considered, which depends rationally on the eigenvalue parameter. Estimates for the eigenvalues and especially for the embedded eigenvalues are proved. Moreover, conditions for the non-existence of embedded eigenvalues are given.

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