On attainability of the lower bound of the minimal eigenvalue of a Sturm–Liouville problem with weighted integral conditions on the potential

S. S. Ezhak, M. Yu. Telnova

Plekhanov Russian State University of Economics, Moscow

Abstract: We consider a Sturm–Liouville problem on $[0, 1]$ with Dirichlet boundary conditions and weighted integral conditions on the potential, where one of the conditions means that the potential may have singularities of different orders at the endpoints of the segment $[0, 1]$. We study sharp lower estimates for the first eigenvalue of the problem for some values of one the parameters of the integral conditions.

Keywords: Sturm–Liouville problem, first eigenvalue, weighted integral condition, variational principle, boundary-value problem

UDC: 517.9

MSC: 34L15

DOI: 10.36535/2782-4438-2025-244-46-54