Svetlana Ezhak, Maria Telnova

On One Upper Estimate for the First Eigenvalue of a Sturm-Liouville Problem with Dirichlet Boundary Conditions and a Weighted Integral Condition

abstract:
We consider a Sturm-Liouville problem on the interval $(0,1)$ with Dirichlet boundary conditions and a weighted integral condition on the potential which may have singularities of different orders at the end-points of the interval $(0,1)$. One upper estimate for the first eigenvalue for some values of parameters in the integral condition is obtained.

Mathematics Subject Classification: 34L15

Key words and phrases: Sturm-Liouville problem, first eigenvalue, Dirichlet boundary conditions, weighted integral condition, minimization of the functional, variational principle, boundary-value problem