Estimates of eigenvalues of Schr\"{o}dinger operators on the half-line with complex-valued potentials

Estimates for eigenvalues of Schr"{o}dinger operators on the half-line with complex-valued potentials are established. Schr"{o}dinger operators with potentials belonging to weak Lebesque’s classes are also considered. The results cover those known previously due to R. L. Frank, A. Laptev and R. Seiringer [In spectral theory and analysis, vol. 214, Oper. Theory Adv. Appl., pag. 39-44; Birkh"{a}user/Springer Basel.]