On the completeness of the system of root vectors of the Sturm-Liouville operator with general boundary conditions

We study general boundary value problems with nondegenerate characteristic determinant Δ(λ) for the Sturm-Liouville equation on the interval 0, 1]. Necessary and sufficient conditions for the completeness of root vectors are obtained in terms of the potential. In particular, it is shown that if Δ(λ) ≠ const, q(·) ∈ C ^k 0, 1] for some k ? 0, and q ^(k)(0) ≠ (?1) ^k q ^(k)(1), then the system of root vectors is complete and minimal in L ^p 0, 1] for p ∈ 1,∞).