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(·) ∈ Ck[0, 1] for some k ⩾ 0, and q(k)(0) ≠ (−1)kq(k)(1), then the system of root vectors is complete and minimal in Lp[0, 1] for p ∈ [1,∞).