Estimates for the first eigenvalue of the Sturm–Liouville problem with potentials in weighted spaces

We consider the Sturm–Liouville problem on the interval $[0,1]$ with the Dirichlet boundary conditions and a weighted integral condition on the potential function, which allows the potential to have singularities of different orders at the end-points. For some values of the parameters of the weight functions, estimates are obtained for the first eigenvalue of this problem, and a method is proposed for finding precise bounds for this eigenvalue in some cases.