On the Eigenvalues and Eigenfunctions of the Sturm–Liouville Operator with a Singular Potential

In this paper we consider the Sturm–Liouville operators generated by the differential expression $-y+q(x)y$ and by Dirichlet boundary conditions on the closed interval $[0,\pi]$. Here $q(x)$ is a distribution of first order, i.e., $\int q(x)dx\in L_2[0,\pi]$. Asymptotic formulas for the eigenvalues and eigenfunctions of such operators which depend on the smoothness degree of $q(x)$ are obtained.