Asymptotics of eigenvalues for regular Sturm-Liouville problems with eigenvalue parameter in the boundary condition

In this paper we obtain asymptotic estimates of eigenvalues for regular Sturm-Liouville problems having the eigenparameter in the boundary condition. The method is based on an iterative procedure solving the associated Riccati equation and producing an asymptotic expansion of the solution in the higher powers of 1/λ1/2 as λ→∞.