We obtain the asymptotic formulas for the eigenvalues and eigenfunctions of the Sturm-Liouville operators with some regular boundary conditions. Using these formulas, we find sufficient conditions on the potential q such that the root functions of these operators do not form a Riesz basis. MSC: 34L05; 34L20

We give a new approach for the estimations of the eigenvalues of non-self-adjoint Sturm-Liouville operators with periodic and antiperiodic boundary conditions. Moreover, we give error estimations, and finally we present some numerical examples.

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We give a new approach for the estimations of the eigenvalues of non-selfadjoint Sturm-Liouville operators with regular but not strongly regular boundary conditions. Moreover we give the error estimations.

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