Asymptotics for eigenvalues of Sturm - Liouville operator with periodic boundary conditions

We employ the similar operators method for studying the spectral properties of the Sturm-Liouville operator generated by the differential expression 𝑙(𝑦) = -𝑦 ′′ -𝑣𝑦 with a complex potential 𝑣 and subject to periodic boundary conditions 𝑦(0) = 𝑦(2𝜋), 𝑦 ′ (0) = 𝑦 ′ (2𝜋).We obtain the results on the asymptotics for the spectrum of the operator.